Parallel matrix function evaluation via initial value ODE modeling

DOI10.1016/j.camwa.2016.04.036zbMath1443.34052arXiv1505.07959OpenAlexW1624629611MaRDI QIDQ2007305

Jean-Paul Chehab, Madalina Petcu

Publication date: 12 October 2020

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.07959

zbMATH Keywords

ODEsfunctions of matricesparareal methods

Mathematics Subject Classification ID

Stability of solutions to ordinary differential equations (34D20) Parallel numerical computation (65Y05)

Related Items (3)

Sparse approximations of matrix functions via numerical integration of ODEs ⋮ A parareal algorithm for a highly oscillating Vlasov-Poisson system with reduced models for the coarse solving ⋮ A parallel spectral deferred correction method for first-order evolution problems

Uses Software

• PARAEXP
• mftoolbox

Cites Work

• Residual methods for the large-scale matrix \(p\)th root and some related problems
• Decay bounds and \(O(n)\) algorithms for approximating functions of sparse matrices
• A new inversion-free method for a rational matrix equation
• A parallel block cyclic reduction algorithm for the fast solution of elliptic equations
• Inexact and truncated parareal-in-time Krylov subspace methods for parabolic optimal control problems
• Convergence properties of some block Krylov subspace methods for multiple linear systems
• Chebyshev rational approximations to \(e^{-x}\) in \([0,+\infty)\) and applications to heat-conduction problems
• Differential equations and solution of linear systems
• Efficient algorithms for the matrix cosine and sine
• Résolution d'EDP par un schéma en temps «pararéel »
• Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection
• Efficient and Stable Arnoldi Restarts for Matrix Functions Based on Quadrature
• Time-parallel implicit integrators for the near-real-time prediction of linear structural dynamic responses
• Analysis of a Krylov subspace enhanced parareal algorithm for linear problems
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
• Unconditionally stable scheme for Riccati equation
• Control Perspectives on Numerical Algorithms and Matrix Problems
• PARAEXP: A Parallel Integrator for Linear Initial-Value Problems
• Analysis of the Parareal Time‐Parallel Time‐Integration Method
• Functions of Matrices
• Analysis of a Modified Parareal Algorithm for Second-Order Ordinary Differential Equations

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