Solving engineering models using hyperbolic matrix functions

•A method for computing hyperbolic matrix functions based on Hermite matrix polynomial expansions is presented.•A new error bound analysis is given.•A theoretical estimate for the optimal value of its parameters is obtained.•An efficient and highly-accurate algorithm (implemented in MATLAB) is prese...

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Vydáno v:Applied mathematical modelling Ročník 40; číslo 4; s. 2837 - 2844
Hlavní autoři: Defez, Emilio, Sastre, Jorge, Ibáñez, Javier, Peinado, Jesús
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 15.02.2016
Témata:
Algorithms
Computation
Estimates
Hermite matrix polynomial
Hermite polynomials
Hyperbolic matrix functions
Mathematical analysis
Mathematical models
Matlab
Optimization
Series expansion
Hermite matrix polynomial
Series expansion
Hyperbolic matrix functions
ISSN:0307-904X
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Shrnutí:•A method for computing hyperbolic matrix functions based on Hermite matrix polynomial expansions is presented.•A new error bound analysis is given.•A theoretical estimate for the optimal value of its parameters is obtained.•An efficient and highly-accurate algorithm (implemented in MATLAB) is presented.•A parallel implementation for large scale problems was developed. In this paper a method for computing hyperbolic matrix functions based on Hermite matrix polynomial expansions is outlined. Hermite series truncation together with Paterson–Stockmeyer method allow to compute the hyperbolic matrix cosine efficiently. A theoretical estimate for the optimal value of its parameters is obtained. An efficient and highly-accurate Hermite algorithm and a MATLAB implementation have been developed. The MATLAB implementation has been compared with the MATLAB function funm on matrices of different dimensions, obtaining lower execution time and higher accuracy in most cases. To do this we used an NVIDIA Tesla K20 GPGPU card, the CUDA environment and MATLAB. With this implementation we get much better performance for large scale problems.
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ISSN:0307-904X
DOI:10.1016/j.apm.2015.09.050