APPROXIMATION OF THE LINEAR COMBINATION OF <i>φ</i>-FUNCTIONS USING THE BLOCK SHIFT-AND-INVERT KRYLOV SUBSPACE METHOD

DOI10.11948/2017085zbMath1454.65027OpenAlexW2762515245MaRDI QIDQ5121516

Dongping Li, Yuhao Cong

Publication date: 15 September 2020

Published in: Journal of Applied Analysis & Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.11948/2017085

zbMATH Keywords

a posteriori error estimatesmatrix exponentialexponential integratorsblock shift-and-invert Krylov subspace methods

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical computation of matrix exponential and similar matrix functions (65F60)

Related Items (1)

Efficient and accurate computation for the \(\varphi\)-functions arising from exponential integrators

Uses Software

• Expokit
• Algorithm 919
• MATLAB expm
• phipm
• mftoolbox

Cites Work

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• Block Krylov subspace methods for approximating the linear combination of \(\varphi\)-functions arising in exponential integrators
• The scaling and modified squaring method for matrix functions related to the exponential
• Applications of the Lanczos method
• A Krylov projection method for systems of ODEs
• Resolvent Krylov subspace approximation to operator functions
• RD-rational approximations of the matrix exponential
• A posteriori error estimates of Krylov subspace approximations to matrix functions
• Residual, Restarting, and Richardson Iteration for the Matrix Exponential
• Convergence Analysis of an Extended Krylov Subspace Method for the Approximation of Operator Functions in Exponential Integrators
• Exponential integrators
• Efficient and Stable Arnoldi Restarts for Matrix Functions Based on Quadrature
• A block Krylov subspace time-exact solution method for linear ordinary differential equation systems
• Algorithm 919
• On Adaptive Choice of Shifts in Rational Krylov Subspace Reduction of Evolutionary Problems
• A new investigation of the extended Krylov subspace method for matrix function evaluations
• Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators
• On Restart and Error Estimation for Krylov Approximation of $w=f(A)v$
• A New Scaling and Squaring Algorithm for the Matrix Exponential
• Approximation of Large-Scale Dynamical Systems
• Structural dynamics analysis using an unsymmetric block Lanczos algorithm
• Analysis of Some Krylov Subspace Approximations to the Matrix Exponential Operator
• Expokit
• On Krylov Subspace Approximations to the Matrix Exponential Operator
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
• The restarted shift-and-invert Krylov method for matrix functions
• The Scaling and Squaring Method for the Matrix Exponential Revisited
• A Restarted Krylov Subspace Method for the Evaluation of Matrix Functions
• Functions of Matrices
• Preconditioning Lanczos Approximations to the Matrix Exponential
• An interpolatory approximation of the matrix exponential based on Faber polynomials

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