Fetching the paper…
Reading the bibliography…
We analyze randomized matrix-free quadrature algorithms for spectrum and spectral sum approximation.
“On Approximation by Trigonometric Sums and Polynomials”
Dunham Jackson · 1912
Earlier work this paper cites.
Diego Granziol, Xingchen Wan and Timur Garipov · 1912
Earlier work this paper cites.
“Fast polynomial transforms based on Toeplitz and Hankel matrices”
Alex Townsend, Marcus Webb and Sheehan Olver · 1934
Earlier work this paper cites.
“Orthogonal polynomials”
Gabor Szegö · 1939
Earlier work this paper cites.
“A note on the summation of Chebyshev series”
C.. Clenshaw · 1955
Earlier work this paper cites.
“On the Construction of Gaussian Quadrature Rules from Modified Moments”
Walter Gautschi · 1970
Earlier work this paper cites.
“Practical use of the symmetric Lanczos process with re-orthogonalization”
C.. Paige · 1970
Earlier work this paper cites.
“An algorithm for Gaussian quadrature given modified moments”
R.. Sack and A.. Donovan · 1971
Earlier work this paper cites.
“Modified Moments for Harmonic Solids”
John. Wheeler and Carl Blumstein · 1972
Earlier work this paper cites.
“Error Analysis of the Lanczos Algorithm for Tridiagonalizing a Symmetric Matrix”
Christopher Paige · 1976
Earlier work this paper cites.
“The Lanczos algorithm with selective orthogonalization”
Beresford Parlet and David. Scott · 1979
Earlier work this paper cites.
“Accuracy and effectiveness of the Lanczos algorithm for the symmetric eigenproblem”
Christopher Paige · 1980
Earlier work this paper cites.
“An introduction to the approximation of functions”, Dover books on advanced mathematics
Theodore. Rivlin · 1981
Earlier work this paper cites.
“On the sensitivity of orthogonal polynomials to perturbations in the moments”
Walter Gautschi · 1986
Earlier work this paper cites.
“Un algorithme rapide pour le calcul de la trace de l’inverse d’une grande matrice”, 1987
Didier Girard · 1987
Earlier work this paper cites.
“The Eigenvalues of Mega-dimensional Matrices”
John Skilling · 1989
Earlier work this paper cites.
“Behavior of slightly perturbed Lanczos and conjugate-gradient recurrences”
Anne Greenbaum · 1989
Earlier work this paper cites.
“The Eigenvalues of Mega-dimensional Matrices”
John Skilling · 1989
Earlier work this paper cites.
“On generating polynomials which are orthogonal over several intervals”
Bernd Fischer and Gene. Golub · 1991
Earlier work this paper cites.
“On generating polynomials which are orthogonal over several intervals”
Bernd Fischer and Gene. Golub · 1991
Earlier work this paper cites.
“On the real convergence rate of the conjugate gradient method”
Zdenek Strakos · 1991
Earlier work this paper cites.
“Theory of approximation”
N.. Achieser · 1992
Earlier work this paper cites.
“Open questions in the convergence analysis of the Lanczos process for the real symmetric eigenvalue problem”
Zdenek Strakos and Anne Greenbaum · 1992
Earlier work this paper cites.
“Densities of states of mega-dimensional Hamiltonian matrices”
R.N. Silver and H. Röder · 1994
Earlier work this paper cites.
“Lanczos method for the calculation of finite-temperature quantities in correlated systems”
J. Jaklič and P. Prelovšek · 1994
Earlier work this paper cites.
“Densities of states of mega-dimensional Hamiltonian matrices”
R.N. Silver and H. Röder · 1994
Earlier work this paper cites.
“Some large-scale matrix computation problems”
Zhaojun Bai, Gark Fahey and Gene Golub · 1996
Earlier work this paper cites.
“Kernel Polynomial Approximations for Densities of States and Spectral Functions”
R.N. Silver, H. Roeder, A.F. Voter and J.D. Kress · 1996
Earlier work this paper cites.
“The Simple Lanczos Procedure: Estimates of the Error of the Gauss Quadrature Formula and Their Applications”
L.. Knizhnerman · 1996
Earlier work this paper cites.
“Kernel Polynomial Approximations for Densities of States and Spectral Functions”
R.N. Silver, H. Roeder, A.F. Voter and J.D. Kress · 1996
Earlier work this paper cites.
“Iterative Methods for Solving Linear Systems”
Anne Greenbaum · 1997
Earlier work this paper cites.
“Iterative Methods for Solving Linear Systems”
Anne Greenbaum · 1997
Cited alongside, same era.
“No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices”
Z.. Bai and Jack. Silverstein · 1998
Cited alongside, same era.
“Introduction to approximation theory”
Elliott. Cheney · 2000
Cited alongside, same era.
“Low-temperature Lanczos method for strongly correlated systems”
Markus Aichhorn, Maria Daghofer, Hans Evertz and Wolfgang von Linden · 2003
Cited alongside, same era.
“Orthogonal polynomials: computation and approximation”, Numerical mathematics and scientific computation
Walter Gautschi · 2004
Cited alongside, same era.
“Entanglement and the foundations of statistical mechanics”
Sandu Popescu, Anthony. Short and Andreas Winter · 2006
“Estimating the Spectral Density of Large Implicit Matrices”, 2018
Ryan. Adams et al · 2018
Later among the works it cites.
“Approximating the Spectrum of a Graph”
David Cohen-Steiner, Weihao Kong, Christian Sohler and Gregory Valiant · 2018
Later among the works it cites.
“High-Dimensional Probability”
Roman Vershynin · 2018
Later among the works it cites.
“An Investigation into Neural Net Optimization via Hessian Eigenvalue Density”
Behrooz Ghorbani, Shankar Krishnan and Ying Xiao · 2019
Later among the works it cites.
“Approximation Theory and Approximation Practice, Extended Edition”
Lloyd. Trefethen · 2019
Later among the works it cites.
“Approximation Theory and Approximation Practice, Extended Edition”
Lloyd. Trefethen · 2019
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
“The kernel polynomial method”
Alexander Weiße, Gerhard Wellein, Andreas Alvermann and Holger Fehske · 2006
Cited alongside, same era.
“The Lanczos and Conjugate Gradient Algorithms”
Gérard Meurant · 2006
Cited alongside, same era.
“The kernel polynomial method”
Alexander Weiße, Gerhard Wellein, Andreas Alvermann and Holger Fehske · 2006
Cited alongside, same era.
“The kink phenomenon in Fejér and Clenshaw–Curtis quadrature”
J… Weideman and L.. Trefethen · 2007
Cited alongside, same era.
“On sensitivity of Gauss–Christoffel quadrature”
Dianne. O’Leary, Zdeněk Strakoš and Petr Tichý · 2007
Cited alongside, same era.
“Is Gauss Quadrature Better than Clenshaw–Curtis?”
Lloyd. Trefethen · 2008
Cited alongside, same era.
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”
Katsuhiro Morita and Takami Tohyama · 2020
Later among the works it cites.
“Accuracy of the finite-temperature Lanczos method compared to simple typicality-based estimates”
Jürgen Schnack, Johannes Richter and Robin Steinigeweg · 2020
Later among the works it cites.
“An adaptive s s -step conjugate gradient algorithm with dynamic basis updating”
Erin. Carson · 2020
Later among the works it cites.
“On Randomized Trace Estimates for Indefinite Matrices with an Application to Determinants”
Alice Cortinovis and Daniel Kressner · 2021
Later among the works it cites.
“Analysis of stochastic Lanczos quadrature for spectrum approximation”
Tyler Chen, Thomas Trogdon and Shashanka Ubaru · 2021
Later among the works it cites.
“Randomized block Krylov subspace methods for trace and log-determinant estimators”
Hanyu Li and Yuanyang Zhu · 2021
Later among the works it cites.
“Hutch++: Optimal Stochastic Trace Estimation”
Raphael. Meyer, Cameron Musco, Christopher Musco and David. Woodruff · 2021
Later among the works it cites.
“Accuracy of the typicality approach using Chebyshev polynomials”
Henrik Schlüter et al · 2021
Later among the works it cites.
“Spectra of Jacobi Operators via Connection Coefficient Matrices”
Marcus Webb and Sheehan Olver · 2021
Later among the works it cites.
“Analysis of stochastic Lanczos quadrature for spectrum approximation”
Tyler Chen, Thomas Trogdon and Shashanka Ubaru · 2021
Later among the works it cites.
“Faster stochastic trace estimation with a Chebyshev product identity”
Eric Hallman · 2021
Later among the works it cites.
“Spectra of Jacobi Operators via Connection Coefficient Matrices”
Marcus Webb and Sheehan Olver · 2021
Later among the works it cites.
“Sublinear time spectral density estimation” arXiv cs.DS 2104.03461
Vladimir Braverman, Aditya Krishnan and Christopher Musco · 2022
Closest in time.
“Improved Variants of the Hutch++ Algorithm for Trace Estimation”
David Persson, Alice Cortinovis and Daniel Kressner · 2022
Closest in time.
“Randomized low-rank approximation of monotone matrix functions”, 2022
David Persson and Daniel Kressner · 2022
Closest in time.
“Sublinear time spectral density estimation” arXiv cs.DS 2104.03461
Vladimir Braverman, Aditya Krishnan and Christopher Musco · 2022
Closest in time.
“Krylov-Aware Stochastic Trace Estimation”
Tyler Chen and Eric Hallman · 2023
Closest in time.
“A spectrum adaptive kernel polynomial method”
Tyler Chen · 2023
Closest in time.
“A Riemann–Hilbert Approach to the Perturbation Theory for Orthogonal Polynomials: Applications to Numerical Linear Algebra and Random Matrix Theory”
Xiucai Ding and Thomas Trogdon · 2023
Closest in time.
“A spectrum adaptive kernel polynomial method”
Tyler Chen · 2023
Closest in time.
“Improved Spectral Density Estimation via Explicit and Implicit Deflation”, 2024
Rajarshi Bhattacharjee et al · 2024
Closest in time.
“XTrace: Making the most of every sample in stochastic trace estimation”
Ethan. Epperly, Joel. Tropp and Robert. Webber · 2024
Closest in time.
“Faster Spectral Density Estimation and Sparsification in the Nuclear Norm”
Yujia Jin et al · 2024
Closest in time.
“The Lanczos algorithm for matrix functions: a handbook for scientists”, 2024
Tyler Chen · 2024
Closest in time.