[EN] Trigonometric matrix functions play a fundamental role in second order differential equations. This work presents an algorithm based on Taylor series for computing the matrix cosine. It uses a backward error analysis ...
Trigonometric matrix functions play a fundamental role in second order differential equation systems. This work presents an algorithm for computing the cosine matrix function based on Taylor series and the cosine double ...
[EN] Recently, two general methods for evaluating matrix polynomials requiring one matrix product less than the Paterson-Stockmeyer method were proposed, where the cost of evaluating a matrix polynomial is given asymptotically ...
The matrix exponential plays a fundamental role in the solution of differential systems which appear in different science fields. This paper presents an efficient method for computing matrix exponentials based on Hermite ...
Román Moltó, José Enrique; Alonso Ábalos, José Miguel; Blanquer Espert, Ignacio; Guerrero López, David; Ibáñez González, Jacinto Javier; Ramos Peinado, Enrique; Alvarruiz Bermejo, Fernando(Editorial Universitat Politècnica de València, 2018-06-13)
Este libro recopila un conjunto de ejemplos de programación paralela, presentados de forma didáctica a modo de ejercicios resueltos.Las herramientas utilizadas son OpenMP y MPI,dos de las más utilizadas en la actualidad ...
[EN] In this work we introduce a new method to compute the matrix cosine. It is based on recent new matrix polynomial evaluation methods for the Taylor approximation and a mixed forward and backward error analysis. The ...
This work presents a new algorithm for matrix exponential computation that significantly simplifies a Taylor scaling and squaring algorithm presented previously by the authors, preserving accuracy. A Matlab version of the ...
Defez Candel, Emilio; Ibáñez González, Jacinto Javier; Peinado Pinilla, Jesús; Alonso-Jordá, Pedro; Alonso Abalos, José Miguel(Elsevier, 2022-07)
[EN] There are, currently, very few implementations to compute the hyperbolic cosine of a matrix. This work tries to fill this gap. To this end, we first introduce both a new rational-polynomial Hermite matrix expansion ...
Defez Candel, Emilio; Ibáñez González, Jacinto Javier; Alonso Abalos, José Miguel; Peinado Pinilla, Jesús; Alonso-Jordá, Pedro(R. Company, J. C. Cortés, L. Jódar and E. López-Navarro, 2019-07-12)
Sastre, Jorge; Ibáñez González, Jacinto Javier; Defez Candel, Emilio; Ruiz Martínez, Pedro Antonio(Society for Industrial and Applied Mathematics, 2015)
The matrix exponential plays a fundamental role in linear differential equations
arising in engineering, mechanics, and control theory. The most widely used, and the most generally
efficient, technique for calculating ...
Ruiz Martínez, Pedro Antonio(Universitat Politècnica de València, 2020-02-17)
[ES] El objetivo de esta tesis es el desarrollo de algoritmos e implementaciones innovadoras de altas prestaciones (HPC) para la computación de funciones de matrices basadas en series de polinomios matriciales. En concreto, ...
Defez Candel, Emilio; Tung ., Michael Ming-Sha; Solis Lozano, Francisco Javier; Ibáñez González, Jacinto Javier(Taylor & Francis, 2015)
Many studies of mechanical systems in engineering are based on second-order matrix models.
This work discusses the second-order generalization of previous research on matrix differential
equations dealing with the ...
This paper deals with the construction of approximate solution of first-order matrix linear differential equations using higher-order matrix splines. An estimation of the approximation error, an algorithm for its implementation ...
Defez Candel, Emilio; Ibáñez González, Jacinto Javier; Alonso-Jordá, Pedro; Alonso Abalos, José Miguel; Peinado Pinilla, Jesús(Elsevier, 2022-04)
[EN] We present in this paper a new method based on Bernoulli matrix polynomials to approximate the exponential of a matrix. The developed method has given rise to two new algorithms whose efficiency and precision are ...
Defez Candel, Emilio; Ibáñez González, Jacinto Javier; Alonso Abalos, José Miguel; Alonso-Jordá, Pedro(John Wiley & Sons, 2022-04)
[EN] 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 ...
Defez Candel, Emilio; Ibáñez González, Jacinto Javier; Alonso Abalos, José Miguel; Tung, Michael Ming-Sha; Real-Herraiz, Teresa Pilar(MDPI AG, 2021-09-15)
[EN] Matrix differential equations are at the heart of many science and engineering problems. In this paper, a procedure based on higher-order matrix splines is proposed to provide the approximated numerical solution of ...
Alonso Jordá, Pedro; Boratto, Murilo; Peinado Pinilla, Jesús; Ibáñez González, Jacinto Javier; Sastre Martinez, Jorge(Universitat Politècnica de València, 2014-09-15)
Computing a matrix polynomial is the basic process in the calculation of functions of matrices by the Taylor method. One of the most efficient techniques for computing matrix polynomials is based on the Paterson– Stockmeyer ...
[EN] This work deals with the simulation of a two¿dimensional ideal lattice having simple tetragonal geometry. The harmonic character of the oscillators give rise to a system of second¿order linear differential equations, ...
Differential Matrix Riccati Equations (DMREs) appear in several branches of science such as applied physics and engineering. For example, these equations play a fundamental role in control theory, optimal control, filtering ...
Differential Matrix Riccati Equations play a fundamental role in control theory, for example, in optimal
control, filtering and estimation, decoupling and order reduction, etc. In this paper a piecewise-linearized
method ...