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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| Veröffentlicht in: | Mathematical methods in the applied sciences Jg. 45; H. 6; S. 3239 - 3253 |
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| Sprache: | Englisch |
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Freiburg
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01.04.2022
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| Abstract | 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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| AbstractList | 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. |
| Author | Alonso, José M. Defez, Emilio Ibáñez, Javier Alonso‐Jordá, Pedro |
| Author_xml | – sequence: 1 givenname: Emilio surname: Defez fullname: Defez, Emilio organization: Universitat Politècnica de València – sequence: 2 givenname: Javier orcidid: 0000-0002-6912-4453 surname: Ibáñez fullname: Ibáñez, Javier organization: Universitat Politècnica de València – sequence: 3 givenname: José M. surname: Alonso fullname: Alonso, José M. organization: Universitat Politècnica de València – sequence: 4 givenname: Pedro orcidid: 0000-0002-6882-6592 surname: Alonso‐Jordá fullname: Alonso‐Jordá, Pedro email: palonso@upv.es organization: Universitat Politècnica de València |
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| SubjectTerms | Algorithms Approximation Mathematical analysis matrix exponential and similar functions of matrices Pade approximation Polynomials polynomials and matrices Series expansion Trigonometric functions |
| Title | On Bernoulli series approximation for the matrix cosine |
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