Fetching the paper…
Reading the bibliography…
We introduce an algorithm for estimating the trace of a matrix function $f(\mathbf{A})$ using implicit products with a symmetric matrix $\mathbf{A}$.
The block Lanczos method for computing eigenvalues
G. H. Golub and R. Underwood · 1977
Earlier work this paper cites.
On the perturbation of pseudo-inverses, projections and linear least squares problems
G. W. Stewart · 1977
Earlier work this paper cites.
Un algorithme simple et rapide pour la validation croisée généralisée sur des problèmes de grande taille, 1987
D. Girard · 1987
Earlier work this paper cites.
A stochastic estimator of the trace of the influence matrix for Laplacian smoothing splines
M. F. Hutchinson · 1989
Earlier work this paper cites.
The eigenvalues of mega-dimensional matrices
J. Skilling · 1989
Earlier work this paper cites.
Error bounds in the simple Lanczos procedure for computing functions of symmetric matrices and eigenvalues
V. L. Druskin and L. A. Knizhnerman · 1991
Earlier work this paper cites.
Implicit application of polynomial filters in a k k -step Arnoldi method
D. C. Sorensen · 1992
Earlier work this paper cites.
Some large-scale matrix computation problems
Z. Bai, G. Fahey, and G. Golub · 1996
Earlier work this paper cites.
Bounds for the trace of the inverse and the determinant of symmetric positive definite matrices
Z. Bai and G. Golub · 1996
Earlier work this paper cites.
The simple Lanczos procedure: Estimates of the error of the Gauss quadrature formula and their applications
L. A. Knizhnerman · 1996
Earlier work this paper cites.
Introduction to the Bethe ansatz i
M. Karabach, G. Müller, H. Gould, and J. Tobochnik · 1997
Earlier work this paper cites.
Thick-restart Lanczos method for large symmetric eigenvalue problems
K. Wu and H. Simon · 2000
Earlier work this paper cites.
The concentration of measure phenomenon
M. Ledoux · 2001
Earlier work this paper cites.
A Krylov–Schur algorithm for large eigenproblems
G. W. Stewart · 2002
Earlier work this paper cites.
IRBL: An implicitly restarted block-Lanczos method for large-scale Hermitian eigenproblems
J. Baglama, D. Calvetti, and L. Reichel · 2003
Earlier work this paper cites.
Entanglement and the foundations of statistical mechanics
S. Popescu, A. J. Short, and A. Winter · 2006
Earlier work this paper cites.
The kernel polynomial method
A. Weiße, G. Wellein, A. Alvermann, and H. Fehske · 2006
Earlier work this paper cites.
An estimator for the diagonal of a matrix
C. Bekas, E. Kokiopoulou, and Y. Saad · 2007
Earlier work this paper cites.
Matrix functions
A. Frommer and V. Simoncini · 2008
Earlier work this paper cites.
Stopping criteria for rational matrix functions of Hermitian and symmetric matrices
A. Frommer and V. Simoncini · 2008
Earlier work this paper cites.
Functions of Matrices
N. J. Higham · 2008
Earlier work this paper cites.
Block Krylov–Schur method for large symmetric eigenvalue problems
Y. Zhou and Y. Saad · 2008
Cited alongside, same era.
Error bounds for Lanczos approximations of rational functions of matrices
A. Frommer and V. Simoncini · 2009
Cited alongside, same era.
Matrices, moments and quadrature with applications
G. H. Golub and G. Meurant · 2009
Cited alongside, same era.
A restarted Lanczos approximation to functions of a symmetric matrix
M. D. Ilic, I. W. Turner, and D. P. Simpson · 2009
Cited alongside, same era.
The University of Florida sparse matrix collection
T. A. Davis and Y. Hu · 2011
Cited alongside, same era.
An algorithm for the principal component analysis of large data sets
N. Halko, P.-G. Martinsson, Y. Shkolnisky, and M. Tygert · 2011
Cited alongside, same era.
Structural convergence results for approximation of dominant subspaces from block Krylov spaces
P. Drineas, I. C. Ipsen, E.-M. Kontopoulou, and M. Magdon-Ismail · 2018
Later among the works it cites.
Improved bounds for small-sample estimation
S. Gratton and D. Titley-Peloquin · 2018
Later among the works it cites.
Stability of the Lanczos method for matrix function approximation
C. Musco, C. Musco, and A. Sidford · 2018
Later among the works it cites.
Approximation Theory and Approximation Practice, Extended Edition
L. N. Trefethen · 2019
Later among the works it cites.
Randomized numerical linear algebra: Foundations and algorithms
P.-G. Martinsson and J. A. Tropp · 2020
Later among the works it cites.
Finite-temperature properties of the Kitaev-Heisenberg models on kagome and triangular lattices studied by improved finite-temperature Lanczos methods
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
N. Halko, P.-G. Martinsson, and J. A. Tropp · 2011
Cited alongside, same era.
Introduction to the non-asymptotic analysis of random matrices
R. Vershynin · 2012
Cited alongside, same era.
2-norm error bounds and estimates for Lanczos approximations to linear systems and rational matrix functions
A. Frommer, K. Kahl, T. Lippert, and H. Rittich · 2013
Cited alongside, same era.
Convergence of restarted Krylov subspace methods for Stieltjes functions of matrices
A. Frommer, S. Güttel, and M. Schweitzer · 2014
Cited alongside, same era.
Error bounds and estimates for Krylov subspace approximations of Stieltjes matrix functions
A. Frommer and M. Schweitzer · 2015
Cited alongside, same era.
Randomized block Krylov methods for stronger and faster approximate singular value decomposition
C. Musco and C. Musco · 2015
Cited alongside, same era.
K. Morita and T. Tohyama · 2020
Later among the works it cites.
Accuracy of the finite-temperature Lanczos method compared to simple typicality-based estimates
J. Schnack, J. Richter, and R. Steinigeweg · 2020
Later among the works it cites.
On randomized trace estimates for indefinite matrices with an application to determinants
A. Cortinovis and D. Kressner · 2021
Later among the works it cites.
Thermodynamic behavior of spin-1 Heisenberg chain: a comparative study
M. Faridfar and J. Vahedi · 2021
Later among the works it cites.
A comparison of limited-memory Krylov methods for Stieltjes functions of Hermitian matrices
S. Güttel and M. Schweitzer · 2021
Later among the works it cites.
Randomized block Krylov subspace methods for trace and log-determinant estimators
H. Li and Y. Zhu · 2021
Later among the works it cites.
Hutch++: Optimal stochastic trace estimation
R. A. Meyer, C. Musco, C. Musco, and D. P. Woodruff · 2021
Later among the works it cites.
Stochastic diagonal estimation: probabilistic bounds and an improved algorithm
R. A. Baston and Y. Nakatsukasa · 2022
Closest in time.
Error bounds for Lanczos-based matrix function approximation
T. Chen, A. Greenbaum, C. Musco, and C. Musco · 2022
Closest in time.
Randomized matrix-free quadrature for spectrum and spectral sum approximation
T. Chen, T. Trogdon, and S. Ubaru · 2022
Closest in time.
A multilevel approach to stochastic trace estimation
E. Hallman and D. Troester · 2022
Closest in time.
Improved variants of the Hutch++ algorithm for trace estimation
D. Persson, A. Cortinovis, and D. Kressner · 2022
Closest in time.
Randomized low-rank approximation of monotone matrix functions
D. Persson and D. Kressner · 2022
Closest in time.
A posteriori error bounds for the block-Lanczos method for matrix function approximation
Q. Xu and T. Chen · 2022
Closest in time.
Xtrace: Making the most of every sample in stochastic trace estimation, 2023
E. N. Epperly, J. A. Tropp, and R. J. Webber · 2023
Closest in time.