Higher Order Fréchet Derivatives of Matrix Functions and the Level-2 Condition Number

DOI10.1137/130945259zbMath1308.65066OpenAlexW2025324442WikidataQ56998664 ScholiaQ56998664MaRDI QIDQ2936584

Nicholas J. Higham, Samuel D. Relton

Publication date: 17 December 2014

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

Full work available at URL: https://doi.org/10.1137/130945259

zbMATH Keywords

expmalgorithmMATLABmatrix square rootFréchet derivativenumerical experimentHermitian matrixpartial derivativematrix exponentialmatrix inversematrix functionGâteaux derivativeKronecker formmatrix logarithmhigher-order derivativematrix calculuslevel-2 condition numberlogmsqrtm

Mathematics Subject Classification ID

Hermitian, skew-Hermitian, and related matrices (15B57) Numerical computation of matrix norms, conditioning, scaling (65F35) Numerical computation of matrix exponential and similar matrix functions (65F60)

Related Items (11)

Taylor's theorem for matrix functions with applications to condition number estimation ⋮ Backward error analysis of polynomial approximations for computing the action of the matrix exponential ⋮ A Taylor expansion of the square root matrix function ⋮ On iterative algorithm and perturbation analysis for the nonlinear matrix equation ⋮ A Unifying Framework for Higher Order Derivatives of Matrix Functions ⋮ Structured level-2 condition numbers of matrix functions ⋮ The complex step approximation to the higher order Fréchet derivatives of a matrix function ⋮ Krylov Approximation of Linear ODEs with Polynomial Parameterization ⋮ Testing Matrix Function Algorithms Using Identities ⋮ New Algorithms for Computing the Matrix Sine and Cosine Separately or Simultaneously ⋮ Integral representations for higher-order Fréchet derivatives of matrix functions: quadrature algorithms and new results on the level-2 condition number

Uses Software

• Matlab
• mctoolbox

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