Efficient and accurate algorithms for computing matrix trigonometric functions

DOI10.1016/j.cam.2016.05.015zbMath1416.65126OpenAlexW2405598217MaRDI QIDQ313622

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

Publication date: 12 September 2016

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

Full work available at URL: https://doi.org/10.1016/j.cam.2016.05.015

zbMATH Keywords

Taylor seriesparallel implementationbackward errormatrix cosinematrix sinescaling and squaring method

Mathematics Subject Classification ID

Parallel numerical computation (65Y05) Matrix exponential and similar functions of matrices (15A16) Numerical computation of matrix exponential and similar matrix functions (65F60)

Related Items

Symplectic integrators for second-order linear non-autonomous equations ⋮ Optimality of the Paterson-Stockmeyer method for evaluating matrix polynomials and rational matrix functions ⋮ Fast Taylor polynomial evaluation for the computation of the matrix cosine ⋮ Editorial: Mathematical modeling and computational methods ⋮ Two algorithms for computing the matrix cosine function ⋮ A new efficient and accurate spline algorithm for the matrix exponential computation ⋮ An efficient and accurate algorithm for computing the matrix cosine based on new Hermite approximations ⋮ Arbitrary Precision Algorithms for Computing the Matrix Cosine and its Fréchet Derivative

Uses Software

• Matlab
• BLAS
• CUDA
• CUBLAS
• Eigtool
• Seigtool
• testmatrix
• mftoolbox
• SONEST
• CONEST

Cites Work

• Accurate matrix exponential computation to solve coupled differential models in engineering
• High performance computing of the matrix exponential
• Efficient orthogonal matrix polynomial based method for computing matrix exponential
• Rational approximations of trigonometric matrices with application to second-order systems of differential equations
• Efficient computation of the matrix cosine
• FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation
• An Algorithm for Computing the Matrix Cosine
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
• New Algorithms for Computing the Matrix Sine and Cosine Separately or Simultaneously
• Functions of Matrices
• An updated set of basic linear algebra subprograms (BLAS)
• On the Number of Nonscalar Multiplications Necessary to Evaluate Polynomials