Functions of matrices - theory and computation

@inproceedings{Higham2008FunctionsOM,
  title={Functions of matrices - theory and computation},
  author={Nicholas John Higham},
  year={2008}
}
  • N. Higham
  • Published 2008
  • Computer Science, Mathematics
A thorough and elegant treatment of the theory of matrix functions and numerical methods for computing them, including an overview of applications, new and unpublished research results, and improved algorithms. Key features include a detailed treatment of the matrix sign function and matrix roots; a development of the theory of conditioning and properties of the Frechet derivative; Schur decomposition; block Parlett recurrence; a thorough analysis of the accuracy, stability, and computational… Expand
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TLDR
This book gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic by combining algorithmic derivations, perturbation theory, and rounding error analysis. Expand
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The sign function of a square matrix can be defined in terms of a contour integral or as the result of an iterated map $. Application of this function enables a matrix to be decomposed into twoExpand
SIAM Review
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Accuracy and stability of numerical algorithms (Society for Industrial and Applied
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3 Padé Approximation of Cosine . . . . . . . . . . . . . . . . . . . . . . 290 12.4 Double Angle Algorithm
  • 3 Padé Approximation of Cosine . . . . . . . . . . . . . . . . . . . . . . 290 12.4 Double Angle Algorithm
302 13.2.2 Arnoldi Approximation of f (A)b . . . . . . . . . . . . . . . . . 304 13
  • 302 13.2.2 Arnoldi Approximation of f (A)b . . . . . . . . . . . . . . . . . 304 13
313 14.1.1 Algebras and
  • 1.5 Computing Structured f (A) for Structured A . . . . . . . . . 316 14.2 Exponential Decay of Functions of Banded Matrices . . . . . . . . . . 317 14.3 Approximating Entries of Matrix Functions
321 B.2 Eigenvalues and
  • 328 B.9 Perturbation Expansions for Matrix Inverse . . . . . . . . . . . . . . 328 Copyright ©2008 by the Society for Industrial and Applied Mathematics. This electronic version is for personal use and may not be duplicated or distributed. From "Functions of Matrices: Theory and Computation
8 (a) is for ℓ > m and what can be said about convergence for ℓ < m−1
  • 8 (a) is for ℓ > m and what can be said about convergence for ℓ < m−1
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