On the stability of some algorithms for computing the action of the matrix exponential

DOI10.1016/j.laa.2013.11.003zbMath1282.65054OpenAlexW2069686901MaRDI QIDQ2438468

Thomas M. Fischer

Publication date: 5 March 2014

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2013.11.003

zbMATH Keywords

one-step methodmatrix exponentialbackward stabilityrounding error analysisforward stability

Mathematics Subject Classification ID

Numerical computation of matrix exponential and similar matrix functions (65F60)

Related Items (5)

An Efficient Numerical Scheme for the Solution of a Stochastic Volatility Model Including Contemporaneous Jumps in Finance ⋮ On the algorithm by Al-Mohy and Higham for computing the action of the matrix exponential: a posteriori roundoff error estimation ⋮ Improved numerical solution of multi-asset option pricing problem: a localized RBF-FD approach ⋮ A multiquadric RBF-FD scheme for simulating the financial HHW equation utilizing exponential integrator ⋮ Estimating the condition number of \(f(A)b\)

Uses Software

• mctoolbox
• MATLAB expm

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Aspects of backward error analysis of numerical ODEs
• Evaluating the Fréchet derivative of the matrix exponential
• The life-span of backward error analysis for numerical integrators
• Derivatives of the matrix exponential and their computation
• The Padé method for computing the matrix exponential
• Padé approximation for the exponential of a block triangular matrix
• Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators
• A New Scaling and Squaring Algorithm for the Matrix Exponential
• Computing the Fréchet Derivative of the Matrix Exponential, with an Application to Condition Number Estimation
• Efficient Solution of Parabolic Equations by Krylov Approximation Methods
• Numerical Computation of the Matrix Exponential with Accuracy Estimate
• The Sensitivity of the Matrix Exponential
• Nineteen Dubious Ways to Compute the Exponential of a Matrix
• Backward Error Analysis for Numerical Integrators
• On Krylov Subspace Approximations to the Matrix Exponential Operator
• A Schur--Fréchet Algorithm for Computing the Logarithm and Exponential of a Matrix
• Using Nonorthogonal Lanczos Vectors in the Computation of Matrix Functions
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
• A Schur-Parlett Algorithm for Computing Matrix Functions
• Condition Estimates for Matrix Functions
• Accuracy and Stability of Numerical Algorithms
• The Scaling and Squaring Method for the Matrix Exponential Revisited
• Functions of Matrices
• A Theory of Condition

This page was built for publication: On the stability of some algorithms for computing the action of the matrix exponential