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We present a probabilistic analysis of two Krylov subspace methods for solving linear systems.
J Wishart, The generalised product moment distribution in samples from a normal multivariate population , Biometrika 20A
1928
Earlier work this paper cites.
H H Goldstine and J von Neumann, Numerical inverting of matrices of high order. II , Proceedings of the AMS 2
1951
Earlier work this paper cites.
M Hestenes and E Steifel, Method of Conjugate Gradients for Solving Linear Systems , J. Research Nat. Bur. Standards 20
1952
Earlier work this paper cites.
Stuart Geman, A limit theorem for the norm of random matrices , The Annals of Probability 8
1980
Earlier work this paper cites.
R J Muirhead, Aspects of Multivariate Statistical Theory , Wiley Series in Probability and Statistics, John Wiley & Sons, Inc., Hoboken, NJ, USA, 1982
1982
Earlier work this paper cites.
S Smale, On the average number of steps of the simplex method of linear programming , Mathematical Programming 27
1983
Earlier work this paper cites.
J W Silverstein, The Smallest Eigenvalue of a Large Dimensional Wishart Matrix , The Annals of Probability 13
1985
Earlier work this paper cites.
K H Borgwardt, The simplex method: A probabilistic analysis , Springer–Verlag, Berlin, Heidelberg, 1987
1987
Earlier work this paper cites.
L N Trefethen and D Bau III, Numerical linear algebra , Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1997
1997
Earlier work this paper cites.
Kurt Johansson, On fluctuations of eigenvalues of random Hermitian matrices , Duke Mathematical Journal 91
1998
Earlier work this paper cites.
P Deift, Orthogonal Polynomials and Random Matrices: a Riemann-Hilbert Approach , Amer. Math. Soc., Providence, RI, 2000
2000
Earlier work this paper cites.
B Beckermann and A B J Kuijlaars, Superlinear Convergence of Conjugate Gradients , SIAM Journal on Numerical Analysis 39
2001
Earlier work this paper cites.
KR Davidson and S J Szarek, Local Operator Theory, Random Matrices and Banach Spaces , Handbook of the Geometry of Banach Spaces, Elsevier, 2001, pp. 317–366
2001
Earlier work this paper cites.
D Spielman and S-H Teng, Smoothed analysis of algorithms , Proceedings of the thirty-third annual ACM symposium on Theory of computing - STOC ’01 (New York, New York, USA), ACM Press, 2001, pp. 296–305
2001
Earlier work this paper cites.
I Dumitriu and A Edelman, Matrix models for beta ensembles , Journal of Mathematical Physics 43
2002
Cited alongside, same era.
Z D Bai and J W Silverstein, CLT for linear spectral statistics of large-dimensional sample covariance matrices , Ann. Probab. 32
2004
Cited alongside, same era.
A Edelman and N R Rao, Random matrix theory , Acta Numerica 14
2005
Cited alongside, same era.
by same author, Global spectrum fluctuations for the β \beta -Hermite and β \beta -Laguerre ensembles via matrix models , J. Math. Phys. 47
2006
Cited alongside, same era.
A B J Kuijlaars, Convergence Analysis of Krylov Subspace Iterations with Methods from Potential Theory , SIAM Review 48
2006
Cited alongside, same era.
C W Pfrang, P Deift, and G Menon, How long does it take to compute the eigenvalues of a random symmetric matrix? , Random matrix theory, interacting particle systems, and integrable systems, MSRI Publications 65
2014
Later among the works it cites.
T K Duy and T Shirai, The mean spectral measures of random Jacobi matrices related to Gaussian beta ensembles , Electron. Commun. Probab. 20
2015
Later among the works it cites.
P A Deift, G Menon, and T Trogdon, On the condition number of the critically-scaled Laguerre Unitary Ensemble , Discrete and Continuous Dynamical Systems 36
2016
Later among the works it cites.
G Menon and T Trogdon, Smoothed analysis for the conjugate gradient algorithm , SIGMA 12
2016
Later among the works it cites.
P Deift and T Trogdon, Universality for Eigenvalue Algorithms on Sample Covariance Matrices , SIAM Journal on Numerical Analysis 55
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A Sankar, D A Spielman, and S-H Teng, Smoothed Analysis of the Condition Numbers and Growth Factors of Matrices , SIAM Journal on Matrix Analysis and Applications 28
2006
Cited alongside, same era.
R Vershynin, Introduction to the non-asymptotic analysis of random matrices , Compressed Sensing (Yonina C. Eldar and Gitta Kutyniok, eds.), Cambridge University Press, Cambridge, 2009, pp. 210–268
2009
Cited alongside, same era.
Z Bai and J W Silverstein, Spectral Analysis of Large Dimensional Random Matrices , Springer Series in Statistics, Springer New York, New York, NY, 2010
2010
Cited alongside, same era.
F W J Olver, D W Lozier, R F Boisvert, and C W Clark, NIST Handbook of Mathematical Functions , Cambridge University Press, 2010
2010
Cited alongside, same era.
M Shcherbina, Central limit theorem for linear eigenvalue statistics of the Wigner and sample covariance random matrices , Zh. Mat. Fiz. Anal. Geom. 7
2011
Cited alongside, same era.
S O’Rourke, D Renfrew, and A Soshnikov, On fluctuations of matrix entries of regular functions of Wigner matrices with non-identically distributed entries , J. Theoret. Probab. 26
2013
Cited alongside, same era.
P A Deift, G Menon, S Olver, and T Trogdon, Universality in numerical computations with random data , Proceedings of the National Academy of Sciences 111
2014
Cited alongside, same era.
2017
Later among the works it cites.
L Erdős and H-T Yau, Dynamical approach to random matrix theory , Amer. Math. Soc., Providence, RI, 2017
2017
Later among the works it cites.
A Knowles and J Yin, Anisotropic local laws for random matrices , Probability Theory and Related Fields 169
2017
Later among the works it cites.
by same author, Universality for the Toda Algorithm to Compute the Largest Eigenvalue of a Random Matrix , Communications on Pure and Applied Mathematics 71
2018
Later among the works it cites.
by same author, Universality in numerical computation with random data: Case Studies, Analytical Results and Some Speculations , Abel Symposia, vol. 13, 3 2018, pp. 221–231
2018
Later among the works it cites.
T K Duy, On spectral measures of random Jacobi matrices , Osaka J. Math. 55
2018
Later among the works it cites.
2019
Later among the works it cites.
G Meurant, On prescribing the convergence behavior of the conjugate gradient algorithm , Numerical Algorithms (2019)
2019
Later among the works it cites.