Two algorithms for computing the matrix cosine function

DOI10.1016/j.amc.2017.05.019zbMath1426.65059OpenAlexW2616975313MaRDI QIDQ1740011

Jorge Sastre, Jesús Peinado, Emilio Defez, Pedro Alonso, Jacinto-Javier Ibáñez

Publication date: 29 April 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10251/99127

zbMATH Keywords

Taylor seriesbackward error analysisforward error analysismatrix cosinescaling and recovering method

Mathematics Subject Classification ID

Matrix exponential and similar functions of matrices (15A16) Numerical computation of matrix exponential and similar matrix functions (65F60)

Related Items

New Hermite series expansion for computing the matrix hyperbolic cosine ⋮ Calculating a function of a matrix with a real spectrum ⋮ Optimality of the Paterson-Stockmeyer method for evaluating matrix polynomials and rational matrix functions ⋮ Efficient evaluation of matrix polynomials ⋮ Fast Taylor polynomial evaluation for the computation of the matrix cosine ⋮ On Bernoulli series approximation for the matrix cosine ⋮ An efficient and accurate algorithm for computing the matrix cosine based on new Hermite approximations ⋮ Boosting the computation of the matrix exponential ⋮ On the backward and forward error of approximations of analytic functions and applications to the computation of matrix functions ⋮ Arbitrary Precision Algorithms for Computing the Matrix Cosine and its Fréchet Derivative

Uses Software

• Matlab
• Eigtool
• Seigtool
• testmatrix
• mftoolbox

Cites Work

• Unnamed Item
• Efficient and accurate algorithms for computing matrix trigonometric functions
• Bounds for variable degree rational \(L_\infty\) approximations to the matrix cosine
• High performance computing of the matrix exponential
• Rational approximations of trigonometric matrices with application to second-order systems of differential equations
• Computing matrix functions arising in engineering models with orthogonal matrix polynomials
• Efficient computation of the matrix cosine
• New methods for oscillatory systems based on ARKN methods
• An Algorithm for Computing the Matrix Cosine
• A Block Algorithm for Matrix 1-Norm Estimation, with an Application to 1-Norm Pseudospectra
• New Scaling-Squaring Taylor Algorithms for Computing the Matrix Exponential
• New Algorithms for Computing the Matrix Sine and Cosine Separately or Simultaneously
• Functions of Matrices
• On the Number of Nonscalar Multiplications Necessary to Evaluate Polynomials

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