Error Bounds for Lanczos-Based Matrix Function Approximation

DOI10.1137/21M1427784zbMath1492.65118arXiv2106.09806OpenAlexW3175126076MaRDI QIDQ5863878

Cameron Musco, Tyler Chen, Christopher Musco, Anne Greenbaum

Publication date: 3 June 2022

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.09806

zbMATH Keywords

Krylov subspace methodLanczosmatrix function approximation

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Analysis of algorithms and problem complexity (68Q25) Numerical computation of matrix exponential and similar matrix functions (65F60)

Related Items

Krylov-Aware Stochastic Trace Estimation ⋮ Low-Memory Krylov Subspace Methods for Optimal Rational Matrix Function Approximation

Uses Software

• MNIST

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Error bounds and estimates for Krylov subspace approximations of Stieltjes matrix functions
• Behavior of slightly perturbed Lanczos and conjugate-gradient recurrences
• Accuracy and effectiveness of the Lanczos algorithm for the symmetric eigenproblem
• Comparison of splittings used with the conjugate gradient algorithm
• Error bounds in the simple Lanczos procedure for computing functions of symmetric matrices and eigenvalues
• Computational methods for UV-suppressed fermions
• Numerical methods for the QCDd overlap operator. I: Sign-function and error bounds
• On error estimation in the conjugate gradient method and why it works in finite precision computations
• A study of defect-based error estimates for the Krylov approximation of \(\varphi\)-functions
• Accurate error estimation in CG
• Computable upper error bounds for Krylov approximations to matrix exponentials and associated \(\varphi\)-functions
• Approximating the extreme Ritz values and upper bounds for the \(A\)-norm of the error in CG
• A posteriori error estimates of Krylov subspace approximations to matrix functions
• 2-Norm Error Bounds and Estimates for Lanczos Approximations to Linear Systems and Rational Matrix Functions
• Efficient and Stable Arnoldi Restarts for Matrix Functions Based on Quadrature
• The Exponentially Convergent Trapezoidal Rule
• Efficient estimation of eigenvalue counts in an interval
• A restarted Lanczos approximation to functions of a symmetric matrix
• Euclidean-Norm Error Bounds for SYMMLQ and CG
• The Lanczos and conjugate gradient algorithms in finite precision arithmetic
• Stopping Criteria for Rational Matrix Functions of Hermitian and Symmetric Matrices
• Computing $A^\alpha, \log(A)$, and Related Matrix Functions by Contour Integrals
• On Estimating the Largest Eigenvalue with the Lanczos Algorithm
• Predicting the Behavior of Finite Precision Lanczos and Conjugate Gradient Computations
• Analysis of Some Krylov Subspace Approximations to the Matrix Exponential Operator
• Estimating the Largest Eigenvalue by the Power and Lanczos Algorithms with a Random Start
• Error Analysis of the Lanczos Algorithm for Tridiagonalizing a Symmetric Matrix
• A Divide-and-Conquer Algorithm for the Symmetric Tridiagonal Eigenproblem
• Estimating the Attainable Accuracy of Recursively Computed Residual Methods
• On Krylov Subspace Approximations to the Matrix Exponential Operator
• Using Nonorthogonal Lanczos Vectors in the Computation of Matrix Functions
• Exponential Integrators for Large Systems of Differential Equations
• Fast Estimation of $tr(f(A))$ via Stochastic Lanczos Quadrature
• Stability of the Lanczos Method for Matrix Function Approximation
• Krylov subspace approximation of eigenpairs and matrix functions in exact and computer arithmetic
• Relations between Galerkin and Norm-Minimizing Iterative Methods for Solving Linear Systems
• A Comparison of Limited-memory Krylov Methods for Stieltjes Functions of Hermitian Matrices
• Accuracy of the Lanczos Process for the Eigenproblem and Solution of Equations
• Convergence of Restarted Krylov Subspace Methods for Stieltjes Functions of Matrices
• Functions of Matrices
• Two polynomial methods of calculating functions of symmetric matrices
• Methods of conjugate gradients for solving linear systems

This page was built for publication: Error Bounds for Lanczos-Based Matrix Function Approximation