Taylor's theorem for matrix functions with applications to condition number estimation

DOI10.1016/j.laa.2016.04.010zbMath1338.15016OpenAlexW1949337326WikidataQ59892388 ScholiaQ59892388MaRDI QIDQ286160

Edvin Deadman, Samuel D. Relton

Publication date: 20 May 2016

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2016.04.010

zbMATH Keywords

condition numberremainderFréchet derivativeTaylor polynomialpseudospectrummatrix function

Mathematics Subject Classification ID

Conditioning of matrices (15A12) Matrix exponential and similar functions of matrices (15A16)

Related Items (1)

Free (rational) derivation

Uses Software

• mctoolbox
• Eigtool
• mftoolbox

Cites Work

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• Estimating the matrix \(p\)-norm
• The complex step approximation to the Fréchet derivative of a matrix function
• Rational approximations of trigonometric matrices with application to second-order systems of differential equations
• An Improved Schur--Padé Algorithm for Fractional Powers of a Matrix and Their Fréchet Derivatives
• Higher Order Fréchet Derivatives of Matrix Functions and the Level-2 Condition Number
• Approximation of Matrix-Valued Functions
• Fast Algorithms for the Approximation of the Pseudospectral Abscissa and Pseudospectral Radius of a Matrix
• A pseudospectral mapping theorem
• A Schur-Parlett Algorithm for Computing Matrix Functions
• New Algorithms for Computing the Matrix Sine and Cosine Separately or Simultaneously
• Pseudospectra of the Orr–Sommerfeld Operator
• Functions of Matrices
• Truncation Errors in Pade Approximations to Certain Functions: An Alternative Approach

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