Fetching the paper…
Reading the bibliography…
We present a randomized, inverse-free algorithm for producing an approximate diagonalization of any $n \times n$ matrix pencil $(A,B)$.
Norms and exclusion theorems
F. L. Bauer and C. T. Fike · 1960
Earlier work this paper cites.
Gaussian elimination is not optimal
V. Strassen · 1969
Earlier work this paper cites.
An algorithm for generalized matrix eigenvalue problems
C. B. Moler and G. W. Stewart · 1973
Earlier work this paper cites.
A new similarity transformation method for eigenvalues and eigenvectors
A. Beavers and E. Denman · 1974
Earlier work this paper cites.
Minimal bases of rational vector spaces, with applications to multivariable linear systems
G. D. Forney, Jr · 1975
Earlier work this paper cites.
Gershgorin theory for the generalized eigenvalue problem A x = λ B x {A}x=\lambda{B}x
G. W. Stewart · 1975
Earlier work this paper cites.
The combination shift QZ algorithm
R. C. Ward · 1975
Earlier work this paper cites.
The spectral transformation Lánczos method for the numerical solution of large sparse generalized symmetric eigenvalue problems
T. Ericsson and A. Ruhe · 1980
Earlier work this paper cites.
Linear model reduction and solution of the algebraic Riccati equation by use of the sign function
J. D. Roberts · 1980
Earlier work this paper cites.
Perturbation theorems for the generalized eigenvalue problem
L. Elsner and J. Sun · 1982
Earlier work this paper cites.
A trace minimization algorithm for the generalized eigenvalue problem
A. H. Sameh and J. A. Wisniewski · 1982
Earlier work this paper cites.
Reducing subspaces: Definitions, properties and algorithms
P. Van Dooren · 1983
Earlier work this paper cites.
The spectral variation of pencils of matrices
L. Elsner and P. Lancaster · 1985
Earlier work this paper cites.
A generalization of the matrix-sign-function solution for algebraic Riccati equations
J. D. Gardiner and A. J. Laub · 1986
Earlier work this paper cites.
Rank revealing QR factorizations
T. F. Chan · 1987
Earlier work this paper cites.
Exclusion theorems and the perturbation analysis of the generalized eigenvalue problem
E. K. Chu · 1987
Earlier work this paper cites.
Computing stable eigendecompositions of matrix pencils
J. W. Demmel and B. Kågström · 1987
Earlier work this paper cites.
Eigenvalues and condition numbers of random matrices
A. Edelman · 1988
Earlier work this paper cites.
ESPRIT-estimation of signal parameters via rotational invariance techniques
R. Roy and T. Kailath · 1989
Earlier work this paper cites.
Matrix multiplication via arithmetic progressions
D. Coppersmith and S. Winograd · 1990
Earlier work this paper cites.
Matrix pencil method for estimating parameters of exponentially damped/undamped sinusoids in noise
Y. Hua and T. Sarkar · 1990
Earlier work this paper cites.
Matrix Perturbation Theory
G. W. Stewart and J. Sun · 1990
Cited alongside, same era.
Parallel algorithm for solving some spectral problems of linear algebra
A. N. Malyshev · 1993
Cited alongside, same era.
Updating a rank-revealing ULV decomposition
G. W. Stewart · 1993
Cited alongside, same era.
Spectral portraits for matrix pencils
V. Frayssé, M. Gueury, F. Nicoud, and V. Toumazou · 1996
Cited alongside, same era.
Efficient algorithms for computing a strong rank-revealing QR factorization
M. Gu and S. C. Eisenstat · 1996
Cited alongside, same era.
Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems
E. Hairer and G. Wanner · 1996
Cited alongside, same era.
Random matrices: the distribution of the smallest singular values
T. Tao and V. Vu · 2009
Later among the works it cites.
Minimizing Communication for Eigenproblems and the Singular Value Decomposition
G. Ballard, J. Demmel, and I. Dumitriu · 2011
Later among the works it cites.
Minimizing communication in numerical linear algebra
G. Ballard, J. Demmel, O. Holtz, and O. Schwartz · 2011
Later among the works it cites.
Smoothed analysis of symmetric random matrices with continuous distributions
B. Farrell and R. Vershynin · 2012
Later among the works it cites.
Matrix Analysis
R. A. Horn and C. R. Johnson · 2012
Later among the works it cites.
A sharp version of Bauer–Fike’s theorem
X. Shi and Y. Wei · 2012
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
An inverse free parallel spectral divide and conquer algorithm for nonsymmetric eigenproblems
Z. Bai, J. Demmel, and M. Gu · 1997
Cited alongside, same era.
Circular law
Z. D. Bai · 1997
Cited alongside, same era.
Structured backward error and condition of generalized eigenvalue problems
D. J. Higham and N. J. Higham · 1998
Cited alongside, same era.
UTV tools: Matlab templates for rank-revealing UTV decompositions
R. D. Fierro, P. C. Hansen, and P. S. K. Hansen · 1999
Cited alongside, same era.
Performance of the QZ algorithm in the presence of infinite eigenvalues
D. S. Watkins · 2000
Cited alongside, same era.
Accuracy and Stability of Numerical Algorithms
N. J. Higham · 2002
Cited alongside, same era.
Multiplying Matrices Faster than Coppersmith-Winograd
V. V. Williams · 2012
Later among the works it cites.
A parallel QZ algorithm for distributed memory HPC systems
B. Adlerborn, B. Kågström, and D. Kressner · 2014
Later among the works it cites.
Matrix regularizing effects of Gaussian perturbations
M. Aizenman, R. Peled, J. Schenker, M. Shamis, and S. Sodin · 2017
Later among the works it cites.
High-Dimensional Probability: An Introduction with Applications in Data Science
R. Vershynin · 2018
Later among the works it cites.
A comparison of eigenvalue condition numbers for matrix polynomials
L. M. Anguas, M. I. Bueno, and F. M. Dopico · 2019
Later among the works it cites.
A Generalized Randomized Rank-Revealing Factorization
G. Ballard, J. Demmel, I. Dumitriu, and A. Rusciano · 2019
Later among the works it cites.
Solving singular generalized eigenvalue problems by a rank-completing perturbation
M. E. Hochstenbach, C. Mehl, and B. Plestenjak · 2019
Later among the works it cites.
Root polynomials and their role in the theory of matrix polynomials
F. M. Dopico and V. Noferini · 2020
Later among the works it cites.
First-order perturbation theory for eigenvalues and eigenvectors
A. Greenbaum, R.-C. Li, and M. L. Overton · 2020
Later among the works it cites.
Wilkinson’s bus: Weak condition numbers, with an application to singular polynomial eigenproblems
M. Lotz and V. Noferini · 2020
Later among the works it cites.
Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators
L. N. Trefethen and M. Embree · 2020
Later among the works it cites.
Gaussian regularization of the pseudospectrum and Davies’ conjecture
J. Banks, A. Kulkarni, S. Mukherjee, and N. Srivastava · 2021
Later among the works it cites.
Pseudospectral Shattering, the Sign Function, and Diagonalization in Nearly Matrix Multiplication Time
J. Banks, J. Garza-Vargas, A. Kulkarni, and N. Srivastava · 2023
Closest in time.
New Bounds for Matrix Multiplication: from Alpha to Omega
V. V. Williams, Y. Xu, Z. Xu, and R. Zhou · 2023
Closest in time.
Pseudospectral Divide-and-Conquer for the Generalized Eigenvalue Problem
R. Schneider · 2024
Closest in time.