On Bernoulli series approximation for the matrix cosine

This paper presents a new series expansion based on Bernoulli matrix polynomials to approximate the matrix cosine function. An approximation based on this series is not a straightforward exercise since there exist different options to implement such a solution. We dive into these options and include...

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Vydáno v:Mathematical methods in the applied sciences Ročník 45; číslo 6; s. 3239 - 3253
Hlavní autoři: Defez, Emilio, Ibáñez, Javier, Alonso, José M., Alonso‐Jordá, Pedro
Médium: Journal Article
Jazyk:angličtina
Vydáno: Freiburg Wiley Subscription Services, Inc 01.04.2022
Témata:
Algorithms
Approximation
Mathematical analysis
matrix exponential and similar functions of matrices
Pade approximation
Polynomials
polynomials and matrices
Series expansion
Trigonometric functions
ISSN:0170-4214, 1099-1476
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Shrnutí:This paper presents a new series expansion based on Bernoulli matrix polynomials to approximate the matrix cosine function. An approximation based on this series is not a straightforward exercise since there exist different options to implement such a solution. We dive into these options and include a thorough comparative of performance and accuracy in the experimental results section that shows benefits and downsides of each one. Also, a comparison with the Padé approximation is included. The algorithms have been implemented in MATLAB and in CUDA for NVIDIA GPUs.
Bibliografie:ObjectType-Article-1
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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.7041