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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Bibliographic Details
Published in:Mathematical methods in the applied sciences Vol. 45; no. 6; pp. 3239 - 3253
Main Authors: Defez, Emilio, Ibáñez, Javier, Alonso, José M., Alonso‐Jordá, Pedro
Format: Journal Article
Language:English
Published: Freiburg Wiley Subscription Services, Inc 01.04.2022
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.7041