The Structured Condition Number of a Differentiable Map between Matrix Manifolds, with Applications

DOI10.1137/17M1148943zbMath1429.65094OpenAlexW2767005796MaRDI QIDQ5232116

Bahar Arslan, Vanni Noferini, Françoise Tisseur

Publication date: 29 August 2019

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

Full work available at URL: https://doi.org/10.1137/17m1148943

zbMATH Keywords

automorphism groupLie algebracondition numberFréchet derivativebilinear formpolar decompositionJordan algebramatrix functionstructured matricessesquilinear formstructured condition number

Mathematics Subject Classification ID

Numerical computation of matrix norms, conditioning, scaling (65F35) Quadratic and bilinear forms, inner products (15A63) Numerical linear algebra (65F99) Numerical computation of matrix exponential and similar matrix functions (65F60)

Related Items

The condition number of many tensor decompositions is invariant under Tucker compression, Structured condition number for a certain class of functions of non-commuting matrices, The Fréchet derivative of the tensor t-function, Three decompositions of symmetric tensors have similar condition numbers, Structured level-2 condition numbers of matrix functions, On formulae for the Moore-Penrose inverse of a columnwise partitioned matrix, Nearest \(\Omega \)-stable matrix via Riemannian optimization, Some matrix properties preserved by generalized matrix functions, A Formula for the Fréchet Derivative of a Generalized Matrix Function

Uses Software

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Cites Work

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• Minimal properties of Moore-Penrose inverses
• An SVD-like matrix decomposition and its applications
• Several observations on symplectic, Hamiltonian, and skew-Hamiltonian matrices
• Condition
• Computing the Polar Decomposition—with Applications
• The vec-permutation matrix, the vec operator and Kronecker products: a review
• On generalized matrix functions
• Structured conditioning of matrix functions
• Condition Estimates for Matrix Functions
• A Formula for the Fréchet Derivative of a Generalized Matrix Function
• Functions Preserving Matrix Groups and Iterations for the Matrix Square Root
• Functions of Matrices
• Structured Factorizations in Scalar Product Spaces
• A Theory of Condition