A technique for improving the computation of functions of triangular matrices

DOI10.1080/00207160.2022.2067751OpenAlexW3213546589WikidataQ114101706 ScholiaQ114101706MaRDI QIDQ5044145

Amir Sadeghi, João R. Cardoso

Publication date: 24 October 2022

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.09727

zbMATH Keywords

matrix functionsSchur decompositionmatrix logarithmmatrix square rootsmatrix inverse cosinefractional powers of a matrix

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Matrix exponential and similar functions of matrices (15A16)

Uses Software

• MATLAB expm
• mftoolbox

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Optimal control and geodesic flows
• The spectral norm of a nonnegative matrix
• A Schur method for the square root of a matrix
• Rational approximations of trigonometric matrices with application to second-order systems of differential equations
• A numerical study of large sparse matrix exponentials arising in Markov chains.
• Computing the matrix Mittag-Leffler function with applications to fractional calculus
• Ranking hubs and authorities using matrix functions
• Computation of matrix gamma function
• Matrix Inverse Trigonometric and Inverse Hyperbolic Functions: Theory and Algorithms
• A Schur Logarithmic Algorithm for Fractional Powers of Matrices
• An Improved Schur--Padé Algorithm for Fractional Powers of a Matrix and Their Fréchet Derivatives
• The Matrix Unwinding Function, with an Application to Computing the Matrix Exponential
• Improved Inverse Scaling and Squaring Algorithms for the Matrix Logarithm
• A New Scaling and Squaring Algorithm for the Matrix Exponential
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
• A Schur Algorithm for Computing Matrix pth Roots
• A Schur-Parlett Algorithm for Computing Matrix Functions
• A finite element method for quantum graphs
• Condition Estimates for Matrix Functions
• New Algorithms for Computing the Matrix Sine and Cosine Separately or Simultaneously
• An Algorithm for the Matrix Lambert $W$ Function
• The Scaling and Squaring Method for the Matrix Exponential Revisited
• An Analytic Theory of Modeling for a Class of Minimal-Energy Control Systems (Disturbance-Free Case)
• Functions of Matrices

This page was built for publication: A technique for improving the computation of functions of triangular matrices