Accurate Approximation of the Matrix Hyperbolic Cosine Using Bernoulli Polynomials

[EN] This paper presents three different alternatives to evaluate the matrix hyperbolic cosine using Bernoulli matrix polynomials, comparing them from the point of view of accuracy and computational complexity. The first two alternatives are derived from two different Bernoulli series expansions of...

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Detalles Bibliográficos
Autores: Alonso Abalos, José Miguel|||0000-0001-6812-7364, Ibáñez González, Jacinto Javier|||0000-0002-6912-4453, Defez Candel, Emilio|||0000-0002-3303-6371, Alvarruiz Bermejo, Fernando|||0000-0001-5957-9561
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/194483
Acceso en línea:https://riunet.upv.es/handle/10251/194483
Access Level:acceso abierto
Palabra clave:Bernoulli matrix polynomials
Matrix hyperbolic cosine
Matrix functions approximation
MATEMATICA APLICADA
CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL
12.- Garantizar las pautas de consumo y de producción sostenibles
Descripción
Sumario:[EN] This paper presents three different alternatives to evaluate the matrix hyperbolic cosine using Bernoulli matrix polynomials, comparing them from the point of view of accuracy and computational complexity. The first two alternatives are derived from two different Bernoulli series expansions of the matrix hyperbolic cosine, while the third one is based on the approximation of the matrix exponential by means of Bernoulli matrix polynomials. We carry out an analysis of the absolute and relative forward errors incurred in the approximations, deriving corresponding suitable values for the matrix polynomial degree and the scaling factor to be used. Finally, we use a comprehensive matrix testbed to perform a thorough comparison of the alternative approximations, also taking into account other current state-of-the-art approaches. The most accurate and efficient options are identified as results.