The complex step approximation to the Fréchet derivative of a matrix function

DOI10.1007/s11075-009-9323-yzbMath1188.65054OpenAlexW2106713925WikidataQ56998722 ScholiaQ56998722MaRDI QIDQ849151

Awad H. Al-Mohy, Nicholas J. Higham

Publication date: 24 February 2010

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-009-9323-y

zbMATH Keywords

Fréchet derivativematrix functioncomplex step approximation

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Numerical computation of matrix norms, conditioning, scaling (65F35)

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Uses Software

• GEMM
• mctoolbox
• Algorithm 894
• PMAD
• MATLAB expm
• mftoolbox

Cites Work

• Extensions of the first and second complex-step derivative approximations
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• GEMM-based level 3 BLAS
• Exploiting fast matrix multiplication within the level 3 BLAS
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• The Scaling and Squaring Method for the Matrix Exponential Revisited
• Functions of Matrices
• The complex-step derivative approximation
• Numerical Differentiation of Analytic Functions
• Perturbation of the matrix sign function