Fetching the paper…
Reading the bibliography…
Approximating invariant subspaces of generalized eigenvalue problems (GEPs) is a fundamental computational problem at the core of machine learning and scientific computing.
Liii. on lines and planes of closest fit to systems of points in space
Karl Pearson · 1901
Earlier work this paper cites.
Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung)
Hermann Weyl · 1912
Earlier work this paper cites.
Analysis of a complex of statistical variables into principal components
Harold Hotelling · 1933
Earlier work this paper cites.
Norms and exclusion theorems
Friedrich L Bauer and Charles T Fike · 1960
Earlier work this paper cites.
The QR transformation a unitary analogue to the LR transformation—Part 1
John GF Francis · 1961
Earlier work this paper cites.
The QR transformation—Part 2
John GF Francis · 1962
Earlier work this paper cites.
On some algorithms for the solution of the complete eigenvalue problem
Vera N Kublanovskaya · 1962
Earlier work this paper cites.
Self-consistent equations including exchange and correlation effects
Walter Kohn and Lu Jeu Sham · 1965
Earlier work this paper cites.
Global convergene of tridiagonal QR algorithm with origin shifts
James Hardy Wilkinson · 1968
Earlier work this paper cites.
Gaussian-Orbital Basis Sets for the First-Row Transition-Metal Atoms
Harold Basch, C. J. Hornback, and J. W. Moskowitz · 1969
Earlier work this paper cites.
Gaussian elimination is not optimal
Volker Strassen · 1969
Earlier work this paper cites.
The shifted QR algorithm for Hermitian matrices
Theodorus J Dekker and Joseph F Traub · 1971
Earlier work this paper cites.
The computation of eigenvalues and eigenvectors of very large sparse matrices
Christopher Conway Paige · 1971
Earlier work this paper cites.
Fast multiplication of large numbers
Arnold Schönhage and Volker Strassen · 1971
Earlier work this paper cites.
On the sensitivity of the eigenvalue problem ax= λ \lambda bx
Gilbert W Stewart · 1972
Earlier work this paper cites.
Reduction of a band-symmetric generalized eigenvalue problem
Charles R. Crawford · 1973
Earlier work this paper cites.
Nested dissection of a regular finite element mesh
Alan George · 1973
Earlier work this paper cites.
Error and perturbation bounds for subspaces associated with certain eigenvalue problems
Gilbert W Stewart · 1973
Earlier work this paper cites.
Spectra of nearly Hermitian matrices
William Kahan · 1975
Earlier work this paper cites.
Error analysis of the lanczos algorithm for tridiagonalizing a symmetric matrix
Christopher C Paige · 1976
Earlier work this paper cites.
On the perturbation of pseudo-inverses, projections and linear least squares problems
Gilbert W Stewart · 1977
Earlier work this paper cites.
Generalized nested dissection
Richard J Lipton, Donald J Rose, and Robert Endre Tarjan · 1979
Earlier work this paper cites.
Pertubation bounds for the definite generalized eigenvalue problem
Gilbert W Stewart · 1979
Earlier work this paper cites.
Spectra of operators with fixed imaginary parts
Andrzej Pokrzywa · 1981
Earlier work this paper cites.
Bounds on the density of states in disordered systems
Franz Wegner · 1981
Earlier work this paper cites.
Extensions of Lipschitz mappings into a Hilbert space
William B Johnson and Joram Lindenstrauss · 1984
Earlier work this paper cites.
The analysis of a nested dissection algorithm
John R Gilbert and Robert Endre Tarjan · 1986
Earlier work this paper cites.
Three methods for refining estimates of invariant subspaces
James Weldon Demmel · 1987
Earlier work this paper cites.
Computing stable eigendecompositions of matrix pencils
James Weldon Demmel and Bo Kågström · 1987
Earlier work this paper cites.
A note on rounding-error analysis of Cholesky factorization
Andrzej Kiełbasiński · 1987
Earlier work this paper cites.
Neural networks and principal component analysis: Learning from examples without local minima
Pierre Baldi and Kurt Hornik · 1989
Earlier work this paper cites.
Computing invariant subspaces of a regular linear pencil of matrices
Alexander N Malyshev · 1989
Earlier work this paper cites.
On a direct algorithm for computing invariant subspaces with specified eigenvalues
Zhaojun Bai and James Demmel · 1991
Earlier work this paper cites.
Direct calculation of electron density in density-functional theory
Weitao Yang · 1991
Earlier work this paper cites.
Large scale electronic structure calculations
Giulia Galli and Michele Parrinello · 1992
Earlier work this paper cites.
Density functional/Wannier function theory for systems of very many atoms
Walter Kohn · 1993
Earlier work this paper cites.
Parallel algorithm for solving some spectral problems of linear algebra
Alexander N Malyshev · 1993
Earlier work this paper cites.
A divide-and-conquer algorithm for the symmetric tridiagonal eigenproblem
Ming Gu and Stanley C Eisenstat · 1995
Earlier work this paper cites.
The matrix sign function
Charles S Kenney and Alan J Laub · 1995
Earlier work this paper cites.
Principal component neural networks: theory and applications
Konstantinos I Diamantaras and Sun Yuan Kung · 1996
Earlier work this paper cites.
Linear scaling methods for electronic structure calculations and quantum molecular dynamics simulations
Giulia Galli · 1996
Earlier work this paper cites.
Efficient algorithms for computing a strong rank-revealing QR factorization
Ming Gu and Stanley C Eisenstat · 1996
Earlier work this paper cites.
Density functional and density matrix method scaling linearly with the number of atoms
Walter Kohn · 1996
Earlier work this paper cites.
Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
Georg Kresse and Jürgen Furthmüller · 1996
Earlier work this paper cites.
Local fluctuation of the spectrum of a multidimensional Anderson tight binding model
Nariyuki Minami · 1996
Earlier work this paper cites.
An inverse free parallel spectral divide and conquer algorithm for nonsymmetric eigenproblems
Zhaojun Bai, James Demmel, and Ming Gu · 1997
Earlier work this paper cites.
A new method for computing the stable invariant subspace of a real Hamiltonian matrix
Peter Benner, Volker Mehrmann, and Hongguo Xu · 1997
Earlier work this paper cites.
Applied numerical linear algebra
James W Demmel · 1997
Earlier work this paper cites.
Computing an eigenvector with inverse iteration
Ilse CF Ipsen · 1997
Earlier work this paper cites.
Using the matrix sign function to compute invariant subspaces
Zhaojun Bai and James Demmel · 1998
Cited alongside, same era.
Relative perturbation results for eigenvalues and eigenvectors of diagonalisable matrices
Stanley C Eisenstat and Ilse CF Ipsen · 1998
Cited alongside, same era.
Fast monte-carlo algorithms for finding low-rank approximations
Alan Frieze, Ravi Kannan, and Santosh Vempala · 1998
Cited alongside, same era.
The Symmetric Eigenvalue Problem
Beresford N Parlett · 1998
Cited alongside, same era.
Nonlinear component analysis as a kernel eigenvalue problem
Bernhard Schölkopf, Alexander Smola, and Klaus-Robert Müller · 1998
Cited alongside, same era.
Linear Combination of Atomic Orbitals
Tim Clark and Rainer Koch · 1999
Cited alongside, same era.
Matrix Computations
Gene H Golub and Charles F Van Loan · 2013
Later among the works it cites.
Stable and efficient spectral divide and conquer algorithms for the symmetric eigenvalue decomposition and the SVD
Yuji Nakatsukasa and Nicholas J Higham · 2013
Later among the works it cites.
OSNAP: Faster numerical linear algebra algorithms via sparser subspace embeddings
Jelani Nelson and Huy L Nguyên · 2013
Later among the works it cites.
Tighter low-rank approximation via sampling the leveraged element
Srinadh Bhojanapalli, Prateek Jain, and Sujay Sanghavi · 2014
Later among the works it cites.
Near-optimal column-based matrix reconstruction
Christos Boutsidis, Petros Drineas, and Malik Magdon-Ismail · 2014
Later among the works it cites.
cp2k: atomistic simulations of condensed matter systems
Jürg Hutter, Marcella Iannuzzi, Florian Schiffmann, and Joost VandeVondele · 2014
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Linear scaling electronic structure methods
Stefan Goedecker · 1999
Cited alongside, same era.
The complexity of the matrix eigenproblem
Victor Y Pan and Zhao Q Chen · 1999
Cited alongside, same era.
Pinching, trimming, truncating, and averaging of matrices
Rajendra Bhatia · 2000
Cited alongside, same era.
Absolute and relative perturbation bounds for invariant subspaces of matrices
Ilse CF Ipsen · 2000
Cited alongside, same era.
Normalized cuts and image segmentation
Jianbo Shi and Jitendra Malik · 2000
Cited alongside, same era.
Database-friendly random projections
Dimitris Achlioptas · 2001
Cited alongside, same era.
Later among the works it cites.
Sparser Johnson-Lindenstrauss transforms
Daniel M Kane and Jelani Nelson · 2014
Later among the works it cites.
Lossy image compression using singular value decomposition and wavelet difference reduction
Awwal Mohammed Rufai, Gholamreza Anbarjafari, and Hasan Demirel · 2014
Later among the works it cites.
Dimensionality reduction for k-means clustering and low rank approximation
Michael B Cohen, Sam Elder, Cameron Musco, Christopher Musco, and Madalina Persu · 2015
Later among the works it cites.
Randomized block Krylov methods for stronger and faster approximate singular value decomposition
Cameron Musco and Christopher Musco · 2015
Later among the works it cites.
LazySVD: Even faster SVD decomposition yet without agonizing pain
Zeyuan Allen-Zhu and Yuanzhi Li · 2016
Later among the works it cites.
Optimal principal component analysis in distributed and streaming models
Christos Boutsidis, David P Woodruff, and Peilin Zhong · 2016
Later among the works it cites.
Sparsified Cholesky and Multigrid Solvers for Connection Laplacians
Rasmus Kyng, Yin Tat Lee, Richard Peng, Sushant Sachdeva, and Daniel A Spielman · 2016
Later among the works it cites.
Approximate Gaussian Elimination for Laplacians - Fast, Sparse, and Simple
Rasmus Kyng and Sushant Sachdeva · 2016
Later among the works it cites.
Accelerated Newton iteration for roots of black box polynomials
Anand Louis and Santosh S Vempala · 2016
Later among the works it cites.
Superfast divide-and-conquer method and perturbation analysis for structured eigenvalue solutions
James Vogel, Jianlin Xia, Stephen Cauley, and Venkataramanan Balakrishnan · 2016
Later among the works it cites.
Solving the trust-region subproblem by a generalized eigenvalue problem
Satoru Adachi, Satoru Iwata, Yuji Nakatsukasa, and Akiko Takeda · 2017
Later among the works it cites.
Matrix regularizing effects of Gaussian perturbations
Michael Aizenman, Ron Peled, Jeffrey Schenker, Mira Shamis, and Sasha Sodin · 2017
Later among the works it cites.
Low-rank approximation and regression in input sparsity time
Kenneth L Clarkson and David P Woodruff · 2017
Later among the works it cites.
Advanced capabilities for materials modelling with Quantum ESPRESSO
P Giannozzi, O Andreussi, T Brumme, O Bunau, M Buongiorno Nardelli, M Calandra, R Car, C Cavazzoni, D Ceresoli, M Cococcioni, N Colonna, I Carnimeo, A Dal Corso, S de Gironcoli, P Delugas, R A DiStasio, A Ferretti, A Floris, G Fratesi, G Fugallo, R Gebauer, U Gerstmann, F Giustino, T Gorni, J Jia, M Kawamura, H-Y Ko, A Kokalj, E Küçükbenli, M Lazzeri, M Marsili, N Marzari, F Mauri, N L Nguyen, H-V Nguyen, A Otero de-la Roza, L Paulatto, S Poncé, D Rocca, R Sabatini, B Santra, M Schlipf, A P Seitsonen, A Smogunov, I Timrov, T Thonhauser, P Umari, N Vast, X Wu, and S Baroni · 2017
Later among the works it cites.
Optimality of the Johnson-Lindenstrauss lemma
Kasper Green Larsen and Jelani Nelson · 2017
Later among the works it cites.
Progress in Theoretical Study of Metal Halide Perovskite Solar Cell Materials
Zewen Xiao and Yanfa Yan · 2017
Later among the works it cites.
A stable, polynomial-time algorithm for the eigenpair problem
Diego Armentano, Carlos Beltrán, Peter Bürgisser, Felipe Cucker, and Michael Shub · 2018
Later among the works it cites.
A Quasi-Random Approach to Matrix Spectral Analysis
Michael Ben-Or and Lior Eldar · 2018
Later among the works it cites.
Stability of the lanczos method for matrix function approximation
Cameron Musco, Christopher Musco, and Aaron Sidford · 2018
Later among the works it cites.
Tight query complexity lower bounds for PCA via finite sample deformed wigner law
Max Simchowitz, Ahmed El Alaoui, and Benjamin Recht · 2018
Later among the works it cites.
Density Functional Theory for Battery Materials
Qiu He, Bin Yu, Zhaohuai Li, and Yan Zhao · 2019
Later among the works it cites.
Advances in Density-Functional Calculations for Materials Modeling
Reinhard J Maurer, Christoph Freysoldt, Anthony M Reilly, Jan Gerit Brandenburg, Oliver T Hofmann, Torbjörn Björkman, Sébastien Lebègue, and Alexandre Tkatchenko · 2019
Later among the works it cites.
Turning big data into tiny data: Constant-size coresets for k-means, PCA, and projective clustering
Dan Feldman, Melanie Schmidt, and Christian Sohler · 2020
Later among the works it cites.
2-d Materials for Ultrascaled Field-Effect Transistors: One Hundred Candidates under the Ab Initio Microscope
Cedric Klinkert, Áron Szabó, Christian Stieger, Davide Campi, Nicola Marzari, and Mathieu Luisier · 2020
Later among the works it cites.
Gaussian Regularization of the Pseudospectrum and Davies’ Conjecture
Jess Banks, Archit Kulkarni, Satyaki Mukherjee, and Nikhil Srivastava · 2021
Later among the works it cites.
Integer multiplication in time o(nlog \ \backslash ,n)
David Harvey and Joris Van Der Hoeven · 2021
Later among the works it cites.
Pseudospectral Shattering, the Sign Function, and Diagonalization in Nearly Matrix Multiplication Time
Jess Banks, Jorge Garza-Vargas, Archit Kulkarni, and Nikhil Srivastava · 2022
Later among the works it cites.
Global Convergence of Hessenberg Shifted QR II: Numerical Stability
Jess Banks, Jorge Garza-Vargas, and Nikhil Srivastava · 2022
Later among the works it cites.
Jess Banks, Jorge Garza-Vargas, and Nikhil Srivastava · 2022
Later among the works it cites.
Stochastic diagonal estimation: probabilistic bounds and an improved algorithm
Robert A Baston and Yuji Nakatsukasa · 2022
Later among the works it cites.
LoRA: Low-rank adaptation of large language models
Edward J Hu, yelong shen, Phillip Wallis, Zeyuan Allen-Zhu, Yuanzhi Li, Shean Wang, Lu Wang, and Weizhu Chen · 2022
Later among the works it cites.
Approximate Euclidean lengths and distances beyond Johnson-Lindenstrauss
Aleksandros Sobczyk and Mathieu Luisier · 2022
Later among the works it cites.
Generalized Pseudospectral Shattering and Inverse-Free Matrix Pencil Diagonalization
James Demmel, Ioana Dumitriu, and Ryan Schneider · 2023
Closest in time.
Faster matrix multiplication via asymmetric hashing
Ran Duan, Hongxun Wu, and Renfei Zhou · 2023
Closest in time.
When is fast, implicit squaring of A − 1 B {A^{-1}B} stable?
Ryan Schneider · 2023
Closest in time.
The complexity of diagonalization
Nikhil Srivastava · 2023
Closest in time.
More asymmetry yields faster matrix multiplication
Josh Alman, Ran Duan, Virginia Vassilevska Williams, Yinzhan Xu, Zixuan Xu, and Renfei Zhou · 2024
Closest in time.
Global Convergence of Hessenberg Shifted QR I: Exact Arithmetic
Jess Banks, Jorge Garza-Vargas, and Nikhil Srivastava · 2024
Closest in time.
XTrace: Making the Most of Every Sample in Stochastic Trace Estimation
Ethan N Epperly, Joel A Tropp, and Robert J Webber · 2024
Closest in time.
Faster Algorithms for Schatten-p Low Rank Approximation
Praneeth Kacham and David P Woodruff · 2024
Closest in time.
On the unreasonable effectiveness of single vector Krylov methods for low-rank approximation
Raphael Meyer, Cameron Musco, and Christopher Musco · 2024
Closest in time.
New bounds for matrix multiplication: from alpha to omega
Virginia Vassilevska Williams, Yinzhan Xu, Zixuan Xu, and Renfei Zhou · 2024
Closest in time.