Fetching the paper…
Reading the bibliography…
This survey describes probabilistic algorithms for linear algebra computations, such as factorizing matrices and solving linear systems.
1909
Earlier work this paper cites.
[] D. A. Spielman and N. Srivastava (2011), ‘Graph sparsification by effective resistances’, SIAM J. Comput
1926
Earlier work this paper cites.
[] E. J. Nyström (1930), ‘Über Die Praktische Auflösung von Integralgleichungen mit Anwendungen auf Randwertaufgaben’, Acta Math
1930
Earlier work this paper cites.
[] S. Bôchner (1933), ‘Monotone Funktionen, Stieltjessche Integrale und harmonische Analyse’, Math. Ann
1933
Earlier work this paper cites.
[] I. J. Schoenberg (1942), ‘Positive definite functions on spheres’, Duke Math. J
1942
Earlier work this paper cites.
[] M. R. Hestenes and E. Stiefel (1952), Methods of conjugate gradients for solving linear systems
1952
Earlier work this paper cites.
[] M. Kac (1956), Foundations of kinetic theory, in Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954–1955, vol. III
1955
Earlier work this paper cites.
[] W. Kahan (1966), ‘Numerical linear algebra’, Canadian Math. Bull
1966
Earlier work this paper cites.
[] V. Strassen (1969), ‘Gaussian elimination is not optimal’, Numerische mathematik
1969
Earlier work this paper cites.
[] J. Cullum and W. E. Donath (1974), A block generalization of the s s -step Lanczos algorithm, Technical Report Report RC 4845 (21570), IBM Thomas J. Watson Research Center, Yorktown Heights, New York
1974
Earlier work this paper cites.
[] N. Tomczak-Jaegermann (1974), ‘The moduli of smoothness and convexity and the Rademacher averages of trace classes S p ( 1 ≤ p < ∞ ) S_{p}(1\leq p<\infty) ’, Studia Math
1974
Earlier work this paper cites.
[] G. H. Golub and R. Underwood (1977), The block Lanczos method for computing eigenvalues, in Mathematical software, III (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1977)
1977
Earlier work this paper cites.
[] I. J. Good (1977), ‘A new formula for k k -statistics’, Ann. Statist
1977
Earlier work this paper cites.
Corrected reprint of the 1980 original
[] B. N. Parlett (1998), The symmetric eigenvalue problem · 1980
Earlier work this paper cites.
[] G. H. Golub, F. T. Luk and M. L. Overton (1981), ‘A block Lánczos method for computing the singular values of corresponding singular vectors of a matrix’, ACM Trans. Math. Software
1981
Earlier work this paper cites.
[] M. B. Marcus and G. Pisier (1981), Random Fourier series with applications to harmonic analysis
1981
Earlier work this paper cites.
[] B. Efron (1982), The jackknife, the bootstrap and other resampling plans
1982
Earlier work this paper cites.
[] W. B. Johnson and J. Lindenstrauss (1984), Extensions of Lipschitz mappings into a Hilbert space, in Conference in modern analysis and probability (New Haven, Conn., 1982)
1982
Earlier work this paper cites.
Wiley Series in Probability and Mathematical Statistics
[] R. J. Muirhead (1982), Aspects of multivariate statistical theory · 1982
Earlier work this paper cites.
[] E. Oja (1982), ‘A simplified neuron model as a principal component analyzer’, J. Math. Biol
1982
Earlier work this paper cites.
[] N. J. A. Sloane (1983), Encrypting by random rotations, in Cryptography (Burg Feuerstein, 1982)
1982
Earlier work this paper cites.
[] J. D. Dixon (1983), ‘Estimating extremal eigenvalues and condition numbers of matrices’, SIAM J. Numer. Anal
1983
Earlier work this paper cites.
[] B. Carl (1985), ‘Inequalities of Bernstein-Jackson-type and the degree of compactness of operators in Banach spaces’, Ann. Inst. Fourier (Grenoble)
1985
Earlier work this paper cites.
[] J. Barnes and P. Hut (1986), ‘A hierarchical o ( n log n ) o(n\log n) force-calculation algorithm’, Nature
1986
Earlier work this paper cites.
[] Y. Gordon (1988), On Milman’s inequality and random subspaces which escape through a mesh in 𝐑 n {\bf R}^{n} , in Geometric aspects of functional analysis (1986/87)
1986
Earlier work this paper cites.
[] F. Lust-Piquard (1986), ‘Inégalités de Khintchine dans C p ( 1 < p < ∞ ) C_{p}\;(1<p<\infty) ’, C. R. Acad. Sci. Paris Sér. I Math
1986
Earlier work this paper cites.
[] Z. Bai, J. Demmel, J. Dongarra, A. Ruhe and H. van der Vorst (1987), Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide (Software, Environments and Tools)
1987
Earlier work this paper cites.
[] L. Greengard and V. Rokhlin (1987), ‘A fast algorithm for particle simulations’, J. Comput. Phys
1987
Earlier work this paper cites.
Thesis (Ph.D.)–Massachusetts Institute of Technology
[] A. S. Edelman (1989), Eigenvalues and condition numbers of random matrices · 1989
Earlier work this paper cites.
[] D. A. Girard (1989), ‘A fast “Monte Carlo cross-validation” procedure for large least squares problems with noisy data’, Numer. Math
1989
Earlier work this paper cites.
Translated from the 1989 Russian original by P. V. Malyshev and D. V. Malyshev and revised by the authors
[] V. S. Koroljuk and Y. V. Borovskich (1994), Theory of U U -statistics · 1989
Earlier work this paper cites.
[] W. K. Wootters and B. D. Fields (1989), ‘Optimal state-determination by mutually unbiased measurements’, Annals of Physics
1989
Earlier work this paper cites.
[] M. F. Hutchinson (1990), ‘A stochastic estimator of the trace of the influence matrix for Laplacian smoothing splines’, Comm. Statist. Simulation Comput
1990
Earlier work this paper cites.
[] W. D. Joubert and G. F. Carey (1991), Parellelizable restarted iterative methods for nonsymmetric linear systems, Center for Numerical Analysis Report CNA-251, UT-Austin
1991
Earlier work this paper cites.
Isoperimetry and processes
[] M. Ledoux and M. Talagrand (1991), Probability in Banach spaces · 1991
Earlier work this paper cites.
[] M. A. Arcones and E. Gine (1992), ‘On the bootstrap of u u and v v statistics’, Ann. Statist
1992
Earlier work this paper cites.
[] J. Kuczyński and H. Woźniakowski (1992), ‘Estimating the largest eigenvalue by the power and Lanczos algorithms with a random start’, SIAM J. Matrix Anal. Appl
1992
Earlier work this paper cites.
[] G. H. Golub and G. Meurant (1994), Matrices, moments and quadrature, in Numerical analysis 1993 (Dundee, 1993)
1993
Earlier work this paper cites.
[] R. Mathias and G. Stewart (1993), ‘A block {QR} algorithm and the singular value decomposition’, Linear Algebra and its Applications
1993
Earlier work this paper cites.
[] J. S. Rosenthal (1994), ‘Random rotations: characters and random walks on SO ( N ) {\rm SO}(N) ’, Ann. Probab
1994
Earlier work this paper cites.
[] G. Stewart (1994), ‘UTV decompositions’, PITMAN RESEARCH NOTES IN MATHEMATICS SERIES
1994
Earlier work this paper cites.
[] W. L. Briggs and V. E. Henson (1995), The DFT: An Owner’s Manual for the Discrete Fourier Transform
1995
Earlier work this paper cites.
[] N. Linial, E. London and Y. Rabinovich (1995), ‘The geometry of graphs and some of its algorithmic applications’, Combinatorica
1995
Earlier work this paper cites.
[] H. Park and L. Eldén (1995), ‘Downdating the rank-revealing urv decomposition’, SIAM Journal on Matrix Analysis and Applications
1995
Earlier work this paper cites.
[] D. Parker (1995), Random butterfly transformations with applications in computational linear algebra, Technical Report CSD-950023, UCLA
1995
Earlier work this paper cites.
Twenty-eighth Annual ACM Symposium on the Theory of Computing (Philadelphia, PA, 1996)
[] N. Alon, Y. Matias and M. Szegedy (1999), The space complexity of approximating the frequency moments, Vol. 58, pp. 137–147 · 1996
Earlier work this paper cites.
[] M. Gu and S. C. Eisenstat (1996), ‘Efficient algorithms for computing a strong rank-revealing QR factorization’, SIAM J. Sci. Comput
1996
Earlier work this paper cites.
[] R. M. Neal (1996), Priors for Infinite Networks
1996
Earlier work this paper cites.
[] U. Porod (1996), ‘The cut-off phenomenon for random reflections’, Ann. Probab
1996
Earlier work this paper cites.
[] B. Schölkopf, A. Smola and K.-R. Müller (1996), Nonlinear component analysis as a kernel eigenvalue problem, Technical report 44, Max-Planck-Institut für biologische Kybernetik
1996
Earlier work this paper cites.
[] R. Bhatia (1997), Matrix analysis
1997
Earlier work this paper cites.
[] S. Goreinov, N. Zamarashkin and E. Tyrtyshnikov (1997), ‘Pseudo-skeleton approximations by matrices of maximal volume’, Mathematical Notes
1997
Earlier work this paper cites.
[] L. N. Trefethen and D. Bau III (1997), Numerical linear algebra
1997
Earlier work this paper cites.
[] C. H. Bischof and G. Quintana-Ortí (1998), ‘Computing rank-revealing QR factorizations of dense matrices’, ACM Transactions on Mathematical Software
1998
Earlier work this paper cites.
[] Z. Leyk and H. Woźniakowski (1998), ‘Estimating a largest eigenvector by Lanczos and polynomial algorithms with a random start’, Numer. Linear Algebra Appl
1998
Earlier work this paper cites.
Special issue on the Seventeenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (Seattle, WA, 1998)
[] C. H. Papadimitriou, P. Raghavan, H. Tamaki and S. Vempala (2000), Latent semantic indexing: a probabilistic analysis, Vol. 61, pp. 217–235 · 1998
Earlier work this paper cites.
[] G. Stewart (1998), Matrix Algorithms Volume 1: Basic Decompositions
1998
Earlier work this paper cites.
[] R. C. Whaley and J. J. Dongarra (1998), Automatically tuned linear algebra software, in Proceedings of the 1998 ACM/IEEE Conference on Supercomputing
1998
Earlier work this paper cites.
Special issue on PODS 1999 (Philadelphia, PA)
[] N. Alon, P. B. Gibbons, Y. Matias and M. Szegedy (2002), Tracking join and self-join sizes in limited storage, Vol. 64, pp. 719–747 · 1999
Earlier work this paper cites.
[] E. Cohen and D. D. Lewis (1999), ‘Approximating matrix multiplication for pattern recognition tasks’, Journal of Algorithms
1999
Earlier work this paper cites.
[] R. D. Fierro, P. C. Hansen and P. S. K. Hansen (1999), ‘Utv tools: Matlab templates for rank-revealing utv decompositions’, Numerical Algorithms
1999
Earlier work this paper cites.
[] A. Gionis, P. Indyk and R. Motwani (1999), Similarity search in high dimensions via hashing, in Proceedings of the 25th International Conference on Very Large Data Bases
1999
Earlier work this paper cites.
[] W. Hackbusch (1999), ‘A sparse matrix arithmetic based on H-matrices; Part I: Introduction to H-matrices’, Computing
1999
Earlier work this paper cites.
[] P. Indyk and R. Motwani (1999), Approximate nearest neighbors: towards removing the curse of dimensionality, in STOC ’98 (Dallas, TX)
1999
Earlier work this paper cites.
[] M. Rudelson (1999), ‘Random vectors in the isotropic position’, J. Funct. Anal
1999
Earlier work this paper cites.
[] G. Stewart (1999), ‘The QLP approximation to the singular value decomposition’, SIAM Journal on Scientific Computing
1999
Earlier work this paper cites.
Special issue on PODS 2001 (Santa Barbara, CA)
[] D. Achlioptas (2003), Database-friendly random projections: Johnson-Lindenstrauss with binary coins, Vol. 66, pp. 671–687 · 2001
Earlier work this paper cites.
[] D. Achlioptas and F. McSherry (2001), Fast computation of low rank matrix approximations, in Proceedings of the Thirty-Third Annual ACM Symposium on Theory of Computing
2001
Earlier work this paper cites.
[] K. R. Davidson and S. J. Szarek (2001), Local operator theory, random matrices and Banach spaces, in Handbook of the geometry of Banach spaces, Vol. I
2001
Earlier work this paper cites.
[] S. Fine and K. Scheinberg (2001), ‘Efficient SVM training using low-rank kernel representation’, Journal of Machine Learning Research
2001
Earlier work this paper cites.
[] G. R. Grimmett and D. R. Stirzaker (2001), Probability and random processes
2001
Earlier work this paper cites.
[] I. M. Johnstone (2001), ‘On the distribution of the largest eigenvalue in principal components analysis’, Ann. Statist
2001
Earlier work this paper cites.
[] B. Schölkopf and A. Smola (2001), Learning with Kernels
2001
Earlier work this paper cites.
[] G. W. Stewart (2001), Matrix algorithms volume 2: eigensystems
2001
Earlier work this paper cites.
[] C. K. I. Williams and M. Seeger (2001), Using the nyström method to speed up kernel machines, in Advances in Neural Information Processing Systems 13
2001
Earlier work this paper cites.
[] R. Ahlswede and A. Winter (2002), ‘Strong converse for identification via quantum channels’, IEEE Trans. Inform. Theory
2002
Earlier work this paper cites.
[] W. Hackbusch, B. Khoromskij and S. Sauter (2002), On ℋ 2 \mathcal{H}^{2} -matrices, in Lectures on Applied Mathematics
2002
Earlier work this paper cites.
[] S. Kurz, O. Rain and S. Rjasanow (2002), ‘The adaptive cross-approximation technique for the 3d boundary-element method’, IEEE transactions on Magnetics
2002
Earlier work this paper cites.
[] L. Grasedyck and W. Hackbusch (2003), ‘Construction and arithmetics of ℋ \mathcal{H} -matrices’, Computing
2003
Earlier work this paper cites.
Automata, languages and programming
[] M. Charikar, K. Chen and M. Farach-Colton (2004), Finding frequent items in data streams, Vol. 312, pp. 3–15 · 2004
Earlier work this paper cites.
[] A. Frieze, R. Kannan and S. Vempala (2004), ‘Fast Monte-Carlo algorithms for finding low-rank approximations’, J. ACM
2004
Earlier work this paper cites.
[] T. Ando (2005), The Schur complement and its applications
2005
Earlier work this paper cites.
[] F. R. Bach and M. Jordan (2005), Predictive low-rank decomposition for kernel methods, in ICML ’05: Proceedings of the 22Nd International Conference on Machine Learning
2005
Earlier work this paper cites.
[] S. Chandrasekaran, M. Gu and W. Lyons (2005), ‘A fast adaptive solver for hierarchically semiseparable representations’, Calcolo
2005
Earlier work this paper cites.
[] Z. Chen and J. J. Dongarra (2005), ‘Condition numbers of Gaussian random matrices’, SIAM J. Matrix Anal. Appl
2005
Earlier work this paper cites.
[] H. Cheng, Z. Gimbutas, P. Martinsson and V. Rokhlin (2005), ‘On the compression of low rank matrices’, SIAM Journal of Scientific Computing
2005
Earlier work this paper cites.
[] P. Drineas and M. W. Mahoney (2005), ‘On the Nyström method for approximating a Gram matrix for improved kernel-based learning’, J. Mach. Learn. Res
2005
Earlier work this paper cites.
[] P. Martinsson and V. Rokhlin (2005), ‘A fast direct solver for boundary integral equations in two dimensions’, J. Comp. Phys
2005
Earlier work this paper cites.
[] S. Muthukrishnan (2005), ‘Data streams: Algorithms and applications’, Foundations and Trends® in Theoretical Computer Science
2005
Earlier work this paper cites.
[] F. Zhang, ed. (2005), The Schur complement and its applications
2005
Earlier work this paper cites.
[] N. Ailon and B. Chazelle (2006), Approximate nearest neighbors and the fast johnson-lindenstrauss transform, in Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
2006
Earlier work this paper cites.
[] M. Bebendorf and R. Grzhibovskis (2006), ‘Accelerating galerkin bem for linear elasticity using adaptive cross approximation’, Mathematical Methods in the Applied Sciences
2006
Earlier work this paper cites.
[] P. Drineas, R. Kannan and M. W. Mahoney (2006 a
2006
Earlier work this paper cites.
[] P. Drineas, R. Kannan and M. W. Mahoney (2006 b
2006
Earlier work this paper cites.
[] P. Drineas, R. Kannan and M. W. Mahoney (2006 c
2006
Earlier work this paper cites.
[] P. Drineas, M. W. Mahoney and S. Muthukrishnan (2006 d
2006
Earlier work this paper cites.
[] P.-G. Martinsson, V. Rokhlin and M. Tygert (2006 a
2006
Earlier work this paper cites.
[] P. Martinsson, V. Rokhlin and M. Tygert (2006 b
2006
Earlier work this paper cites.
[] A. Sankar, D. A. Spielman and S.-H. Teng (2006), ‘Smoothed analysis of the condition numbers and growth factors of matrices’, SIAM J. Matrix Anal. Appl
2006
Earlier work this paper cites.
[] T. Sarlós (2006), Improved approximation algorithms for large matrices via random projections, in 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS’06)
2006
Earlier work this paper cites.
[] J. A. Tropp, M. B. Wakin, M. F. Duarte, D. Baron and R. G. Baraniuk (2006), Random filters for compressive sampling and reconstruction, in 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings
2006
Earlier work this paper cites.
[] D. Achlioptas and F. McSherry (2007), ‘Fast computation of low-rank matrix approximations’, J. ACM
2007
Cited alongside, same era.
[] J. Demmel, I. Dumitriu and O. Holtz (2007), ‘Fast linear algebra is stable’, Numerische Mathematik
2007
Cited alongside, same era.
[] E. Liberty, F. Woolfe, P.-G. Martinsson, V. Rokhlin and M. Tygert (2007), ‘Randomized algorithms for the low-rank approximation of matrices’, Proc. Natl. Acad. Sci. USA
2007
Cited alongside, same era.
[] F. Mezzadri (2007), ‘How to generate random matrices from the classical compact groups’, Notices Amer. Math. Soc
2007
Cited alongside, same era.
[] M. O’Neil (2007), A new class of analysis-based fast transforms, PhD thesis, Mathematics, Yale University
2007
Cited alongside, same era.
[] M. Pilanci and M. J. Wainwright (2015), ‘Randomized sketches of convex programs with sharp guarantees’, IEEE Trans. Inform. Theory
2015
Later among the works it cites.
[] A. Rudi, R. Camoriano and L. Rosasco (2015), Less is more: Nyström computational regularization, in Advances in Neural Information Processing Systems 28
2015
Later among the works it cites.
[] Y.-L. K. Samo and S. Roberts (2015), ‘Generalized spectral kernels’
2015
Later among the works it cites.
[] B. Sriperumbudur and Z. Szabo (2015), Optimal rates for random fourier features, in Advances in Neural Information Processing Systems 28
2015
Later among the works it cites.
[] C. Thrampoulidis and B. Hassibi (2015), ‘Isotropically random orthogonal matrices: Performance of lasso and minimum conic singular values’
2015
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
[] M. Rudelson and R. Vershynin (2007), ‘Sampling from large matrices: an approach through geometric functional analysis’, J. ACM
2007
Cited alongside, same era.
[] P. Drineas, M. W. Mahoney and S. Muthukrishnan (2008), ‘Relative-error C U R CUR matrix decompositions’, SIAM J. Matrix Anal. Appl
2008
Cited alongside, same era.
[] A. Rahimi and B. Recht (2008), Random features for large-scale kernel machines, in Advances in Neural Information Processing Systems 20
2008
Cited alongside, same era.
[] V. Rokhlin and M. Tygert (2008), ‘A fast randomized algorithm for overdetermined linear least-squares regression’, Proc. Natl. Acad. Sci. USA
2008
Cited alongside, same era.
[] M. Rudelson and R. Vershynin (2008), ‘On sparse reconstruction from Fourier and Gaussian measurements’, Comm. Pure Appl. Math
2008
Cited alongside, same era.
[] F. Woolfe, E. Liberty, V. Rokhlin and M. Tygert (2008), ‘A fast randomized algorithm for the approximation of matrices’, Appl. Comput. Harmon. Anal
2008
Cited alongside, same era.
[] N. Ailon and B. Chazelle (2009), ‘The fast Johnson-Lindenstrauss transform and approximate nearest neighbors’, SIAM J. Comput
2009
Cited alongside, same era.
[] J. A. Tropp (2015), ‘An introduction to matrix concentration inequalities’, Foundations and Trends in Machine Learning
2015
Later among the works it cites.
[] C. Boutsidis, D. P. Woodruff and P. Zhong (2016), Optimal principal component analysis in distributed and streaming models, in Proceedings of the forty-eighth annual ACM symposium on Theory of Computing
2016
Later among the works it cites.
[] M. B. Cohen (2016), Nearly tight oblivious subspace embeddings by trace inequalities, in Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms
2016
Later among the works it cites.
[] T. A. Davis, S. Rajamanickam and W. M. Sid-Lakhdar (2016), ‘A survey of direct methods for sparse linear systems’, Acta Numerica
2016
Later among the works it cites.
[] D. Feldman, M. Volkov and D. Rus (2016), Dimensionality reduction of massive sparse datasets using coresets, in Advances in Neural Information Processing Systems
2016
Later among the works it cites.
[] M. Ghashami, E. Liberty, J. M. Phillips and D. P. Woodruff (2016 a
2016
Later among the works it cites.
[] M. Ghashami, D. J. Perry and J. Phillips (2016 b
2016
Later among the works it cites.
[] D. Kressner, M. Steinlechner and B. Vandereycken (2016), ‘Preconditioned low-rank riemannian optimization for linear systems with tensor product structure’, SIAM Journal on Scientific Computing
2016
Later among the works it cites.
[] R. Kyng and S. Sachdeva (2016), Approximate Gaussian elimination for Laplacians—fast, sparse, and simple, in 57th Annual IEEE Symposium on Foundations of Computer Science—FOCS 2016
2016
Later among the works it cites.
[] R. Kyng, Y. T. Lee, R. Peng, S. Sachdeva and D. A. Spielman (2016), Sparsified Cholesky and multigrid solvers for connection Laplacians, in STOC’16—Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing
2016
Later among the works it cites.
[] P. Martinsson and S. Voronin (2016), ‘A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices’, SIAM Journal on Scientific Computing
2016
Later among the works it cites.
[] P.-G. Martinsson (2016), ‘Compressing rank-structured matrices via randomized sampling’, SIAM Journal on Scientific Computing
2016
Later among the works it cites.
[] M. Pilanci and M. J. Wainwright (2016), ‘Iterative Hessian sketch: fast and accurate solution approximation for constrained least-squares’, J. Mach. Learn. Res
2016
Later among the works it cites.
[] H. Rauhut and R. Ward (2016), ‘Interpolation via weighted ℓ 1 \ell_{1} minimization’, Appl. Comput. Harmon. Anal
2016
Later among the works it cites.
[] D. C. Sorensen and M. Embree (2016), ‘A deim induced cur factorization’, SIAM Journal on Scientific Computing
2016
Later among the works it cites.
[] J. A. Tropp (2016), The expected norm of a sum of independent random matrices: an elementary approach, in High dimensional probability VII
2016
Later among the works it cites.
2016
Later among the works it cites.
[] R. Van Handel (2016), Probability in high dimension, Apc 550 lecture notes, Princeton Univ
2016
Later among the works it cites.
[] H. Avron, K. Clarkson and D. Woodruff (2017), ‘Faster kernel ridge regression using sketching and preconditioning’, SIAM Journal on Matrix Analysis and Applications
2017
Later among the works it cites.
[] M. Baboulin, J. J. Dongarra, A. Rémy, S. Tomov and I. Yamazaki (2017), ‘Solving dense symmetric indefinite systems using gpus’, Concurrency and Computation: Practice and Experience
2017
Later among the works it cites.
[] F. Bach (2017), ‘On the equivalence between kernel quadrature rules and random feature expansions’, Journal of Machine Learning Research
2017
Later among the works it cites.
[] K. Bringmann and K. Panagiotou (2017), ‘Efficient sampling methods for discrete distributions’, Algorithmica
2017
Later among the works it cites.
[] A. Cohen and G. Migliorati (2017), ‘Optimal weighted least-squares methods’, SMAI J. Comput. Math
2017
Later among the works it cites.
[] J. A. Duersch and M. Gu (2017), ‘Randomized qr with column pivoting’, SIAM Journal on Scientific Computing
2017
Later among the works it cites.
[] P. Ghysels, X. S. Li, C. Gorman and F.-H. Rouet (2017), A robust parallel preconditioner for indefinite systems using hierarchical matrices and randomized sampling, in 2017 IEEE International Parallel and Distributed Processing Symposium (IPDPS)
2017
Later among the works it cites.
[] L. Goldstein, I. Nourdin and G. Peccati (2017), ‘Gaussian phase transitions and conic intrinsic volumes: Steining the Steiner formula’, Ann. Appl. Probab
2017
Later among the works it cites.
[] H. Guo, Y. Liu, J. Hu and E. Michielssen (2017), ‘A butterfly-based direct integral-equation solver using hierarchical lu factorization for analyzing scattering from electrically large conducting objects’, IEEE Transactions on Antennas and Propagation
2017
Later among the works it cites.
[] R. Kannan and S. Vempala (2017), ‘Randomized algorithms in numerical linear algebra’, Acta Numerica
2017
Later among the works it cites.
[] W. Kong and G. Valiant (2017), ‘Spectrum estimation from samples’, Ann. Statist
2017
Later among the works it cites.
Thesis (Ph.D.)–Yale University
[] R. Kyng (2017), Approximate Gaussian elimination · 2017
Later among the works it cites.
[] H. Li, G. C. Linderman, A. Szlam, K. P. Stanton, Y. Kluger and M. Tygert (2017), ‘Algorithm 971: an implementation of a randomized algorithm for principal component analysis’, ACM Trans. Math. Software
2017
Later among the works it cites.
[] Y. Li and H. Yang (2017), ‘Interpolative butterfly factorization’, SIAM Journal on Scientific Computing
2017
Later among the works it cites.
[] L.-H. Lim and J. Weare (2017), ‘Fast randomized iteration: Diffusion monte carlo through the lens of numerical linear algebra’, SIAM Review
2017
Later among the works it cites.
[] P. Martinsson, G. Quintana-Ortí, N. Heavner and R. van de Geijn (2017), ‘Householder qr factorization with randomization for column pivoting (hqrrp)’, SIAM Journal on Scientific Computing
2017
Later among the works it cites.
[] M. B. McCoy and J. A. Tropp (2013), The achievable performance of convex demixing, ACM Technical Report 2017-02, Caltech, Pasadena, CA
2017
Later among the works it cites.
[] C. Musco and C. Musco (2017), Recursive sampling for the nystrom method, in Advances in Neural Information Processing Systems 30
2017
Later among the works it cites.
[] V. Y. Pan and L. Zhao (2017), ‘Numerically safe gaussian elimination with no pivoting’, Linear Algebra and its Applications
2017
Later among the works it cites.
[] N. S. Pillai and A. Smith (2017), ‘Kac’s walk on n n -sphere mixes in n log n n\log n steps’, Ann. Appl. Probab
2017
Later among the works it cites.
[] P. Richtárik and M. Takáč (2017), ‘Stochastic reformulations of linear systems: Algorithms and convergence theory’
2017
Later among the works it cites.
[] A. Rudi and L. Rosasco (2017), Generalization properties of learning with random features, in Advances in Neural Information Processing Systems 30
2017
Later among the works it cites.
[] A. Rudi, L. Carratino and L. Rosasco (2017), Falkon: An optimal large scale kernel method, in Advances in Neural Information Processing Systems 30
2017
Later among the works it cites.
[] M. Simchowitz, A. E. Alaoui and B. Recht (2017), ‘On the gap between strict-saddles and true convexity: An omega(log d) lower bound for eigenvector approximation’
2017
Later among the works it cites.
[] T. Trogdon (2017), ‘On spectral and numerical properties of random butterfly matrices’, Appl. Math. Lett
2017
Later among the works it cites.
[] J. A. Tropp, A. Yurtsever, M. Udell and V. Cevher (2017 a
2017
Later among the works it cites.
[] J. A. Tropp, A. Yurtsever, M. Udell and V. Cevher (2017 b
2017
Later among the works it cites.
[] J. A. Tropp, A. Yurtsever, M. Udell and V. Cevher (2017 c
2017
Later among the works it cites.
[] S. Ubaru, J. Chen and Y. Saad (2017), ‘Fast estimation of tr ( f ( A ) ) \text{\tt tr}(f(A)) via stochastic Lanczos quadrature’, SIAM J. Matrix Anal. Appl
2017
Later among the works it cites.
[] S. Voronin and P.-G. Martinsson (2017), ‘Efficient algorithms for cur and interpolative matrix decompositions’, Advances in Computational Mathematics
2017
Later among the works it cites.
[] J. Xiao, M. Gu and J. Langou (2017), Fast parallel randomized qr with column pivoting algorithms for reliable low-rank matrix approximations, in 2017 IEEE 24th International Conference on High Performance Computing (HiPC)
2017
Later among the works it cites.
[] C. D. Yu, J. Levitt, S. Reiz and G. Biros (2017 a
2017
Later among the works it cites.
[] W. Yu, Y. Gu, J. Li, S. Liu and Y. Li (2017 b
2017
Later among the works it cites.
Slides, Workshop on Randomized Numerical Linear Algebra, Simons Institute, UC-Berkeley
[] H. Avron (2018), ‘Randomized Riemannian preconditioning for quadratically constrained problems’ · 2018
Later among the works it cites.
[] E. Dobriban and S. Liu (2018), ‘Asymptotics for sketching in least squares regression’
2018
Later among the works it cites.
IAS/Park City Mathematics Series
[] P. Drineas and M. Mahoney (2018), Lectures on randomized linear algebra, in The Mathematics of Data · 2018
Later among the works it cites.
2018
Later among the works it cites.
[] J. K. Fitzsimons, M. A. Osborne, S. J. Roberts and J. F. Fitzsimons (2018), Improved stochastic trace estimators using mutually unbiased bases, in Uncertainty in Artificial Intelligence: Proceedings of the Thirty-Fourth Conference
2018
Later among the works it cites.
[] A. Gopal and P.-G. Martinsson (2018), ‘The PowerURV algorithm for computing rank-revealing full factorizations’
2018
Later among the works it cites.
[] R. Gower, F. Hanzely, P. Richtarik and S. U. Stich (2018), Accelerated stochastic matrix inversion: General theory and speeding up bfgs rules for faster second-order optimization, in Advances in Neural Information Processing Systems 31
2018
Later among the works it cites.
[] S. Gratton and D. Titley-Peloquin (2018), ‘Improved bounds for small-sample estimation’, SIAM J. Matrix Anal. Appl
2018
Later among the works it cites.
[] Y. Li, H. Yang and L. Ying (2018), ‘Multidimensional butterfly factorization’, Applied and Computational Harmonic Analysis
2018
Later among the works it cites.
IAS/Park City Mathematics Series
[] P.-G. Martinsson (2018), Randomized methods for matrix computations, in The Mathematics of Data · 2018
Later among the works it cites.
[] S. Mendelson, H. Rauhut and R. Ward (2018), ‘Improved bounds for sparse recovery from subsampled random convolutions’, Ann. Appl. Probab
2018
Later among the works it cites.
[] C. Musco, C. Musco and A. Sidford (2018), Stability of the Lanczos method for matrix function approximation, in Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms
2018
Later among the works it cites.
[] S. Oymak and J. A. Tropp (2018), ‘Universality laws for randomized dimension reduction, with applications’, Inf. Inference
2018
Later among the works it cites.
[] A. Rudi, D. Calandriello, L. Carratino and L. Rosasco (2018), On fast leverage score sampling and optimal learning, in Advances in Neural Information Processing Systems 31
2018
Later among the works it cites.
[] Y. Sun, Y. Guo, J. A. Tropp and M. Udell (2018), Tensor random projection for low memory dimension reduction, in NeurIPS Workshop on Relational Representation Learning
2018
Later among the works it cites.
One world, one health
[] J.-F. Ton, S. Flaxman, D. Sejdinovic and S. Bhatt (2018), ‘Spatial mapping with gaussian processes and nonstationary fourier features’, Spatial Statistics · 2018
Later among the works it cites.
[] J. A. Tropp (2018), Analysis of randomized block krylov methods, Under revision
2018
Later among the works it cites.
[] E. Ullah, P. Mianjy, T. V. Marinov and R. Arora (2018), Streaming kernel pca with ℴ ~ ( n ) \tilde{\mathcal{o}}(\sqrt{n}) random features, in Advances in Neural Information Processing Systems 31
2018
Later among the works it cites.
An introduction with applications in data science, With a foreword by Sara van de Geer
[] R. Vershynin (2018), High-dimensional probability · 2018
Later among the works it cites.
[] S. F. D. Waldron (2018), An introduction to finite tight frames
2018
Later among the works it cites.
[] Q. Yuan, M. Gu and B. Li (2018), Superlinear convergence of randomized block lanczos algorithm, in 2018 IEEE International Conference on Data Mining (ICDM)
2018
Later among the works it cites.
[] B. Arras, M. Bachmayr and A. Cohen (2019), ‘Sequential sampling for optimal weighted least squares approximations in hierarchical spaces’, SIAM J. Math. Data Sci
2019
Later among the works it cites.
[] H. Avron, M. Kapralov, C. Musco, C. Musco, A. Velingker and A. Zandieh (2019), A universal sampling method for reconstructing signals with simple fourier transforms, in Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing
2019
Later among the works it cites.
[] P. Baldi and R. Vershynin (2019), ‘Polynomial threshold functions, hyperplane arrangements, and random tensors’, SIAM J. Math. Data Sci
2019
Later among the works it cites.
[] J. Banks, J. G. Vargas, A. Kulkarni and N. Srivastava (2019), ‘Pseudospectral shattering, the sign function, and diagonalization in nearly matrix multiplication time’
2019
Later among the works it cites.
[] Y. Carmon, J. C. Duchi, A. Sidford and K. Tian (2019), A rank-1 sketch for matrix multiplicative weights, in Proceedings of the Thirty-Second Conference on Learning Theory
2019
Later among the works it cites.
[] X. Chen and E. Price (2019), Active regression via linear-sample sparsification, in Proceedings of the Thirty-Second Conference on Learning Theory
2019
Later among the works it cites.
[] T. Dao, A. Gu, M. Eichhorn, A. Rudra and C. Ré (2019), ‘Learning fast algorithms for linear transforms using butterfly factorizations’
2019
Later among the works it cites.
[] P. Hennig and M. A. Osborne (2019), ‘probabilistic-numerics.org’
2019
Later among the works it cites.
[] R. Jin, T. G. Kolda and R. Ward (2019), ‘Faster johnson-lindenstrauss transforms via kronecker products’
2019
Later among the works it cites.
[] R. Kueng (2019), 2-designs minimize variance of trace estimators, Unpublished manuscript
2019
Later among the works it cites.
[] M. E. Lopes (2019), ‘Estimating the algorithmic variance of randomized ensembles via the bootstrap’, Ann. Statist
2019
Later among the works it cites.
[] O. A. Malik and S. Becker (2019), ‘Guarantees for the kronecker fast johnson-lindenstrauss transform using a coherence and sampling argument’
2019
Later among the works it cites.
[] P.-G. Martinsson (2019), Fast Direct Solvers for Elliptic PDEs
2019
Later among the works it cites.
Accepted for publication by ACM TOMS
[] P. Martinsson, G. Quintana Orti and N. Heavner (2019), ‘randUTV: A blocked randomized algorithm for computing a rank-revealing UTV factorization’, arXiv preprint arXiv:1703.00998 · 2019
Later among the works it cites.
https://www.nag.com/content/naglibrary-mark27
[] T. N. A. G. (NAG) (2019), ‘The nag library mark 27’ · 2019
Later among the works it cites.
[] F. Pourkamali-Anaraki and S. Becker (2019), ‘Improved fixed-rank nyström approximation via qr decomposition: Practical and theoretical aspects’, Neurocomputing
2019
Later among the works it cites.
[] G. Strang (2019), Linear algebra and learning from data
2019
Later among the works it cites.
[] Z. Szabo and B. Sriperumbudur (2019), On kernel derivative approximation with random fourier features, in Proceedings of Machine Learning Research
2019
Later among the works it cites.
[] J. A. Tropp (2019), Matrix concentration and computational linear algebra, CMS Lecture Notes 2019-01, Caltech, Pasadena, CA
2019
Later among the works it cites.
[] J. A. Tropp, A. Yurtsever, M. Udell and V. Cevher (2019), ‘Streaming low-rank matrix approximation with an application to scientific simulation’, SIAM J. Sci. Comput
2019
Later among the works it cites.
[] R. Vershynin (2019), ‘Concentration inequalities for random tensors’
2019
Later among the works it cites.
[] S. Wang (2019), ‘Simple and almost assumption-free out-of-sample bound for random feature mapping’
2019
Later among the works it cites.
[] S. Wang, A. Gittens and M. W. Mahoney (2019), ‘Scalable kernel k-means clustering with nyström approximation: Relative-error bounds’, J. Mach. Learn. Res
2019
Later among the works it cites.