This paper describes an approach for solving differential Riccati equations (DRE), by means of the backward differentiation formula (BDF) and resolution of the corresponding implicit equation using Newton’s method with a ...
Differential Riccati equations play a fundamental role in control theory, for example, optimal control, filtering and estimation, decoupling and order reduction, etc. The most popular codes to solve stiff differential ...
In this paper a method for computing hyperbolic matrix sine based
on Hermite matrix polynomial expansions is presented. An error bound analysis is
given
[EN] In this work an accurate and efficient method based on matrix splines for computing
matrix exponential is given. An algorithm and a MATLAB implementation have been
developed and compared with the state-of-the-art ...
Defez Candel, Emilio; Ibáñez González, Jacinto Javier; Alonso Abalos, José Miguel; Peinado Pinilla, Jesús; Sastre, Jorge(Universitat Politècnica de València, 2021-11-30)
[EN] The evaluation of matrix functions plays an important and relevant role in many scientific applications because matrix functions have proven to be an ecient tool in applications such as
reduced order models [1], [2, ...
Differential Riccati equations play a fundamental role in control theory, for example,
optimal control, filtering and estimation, decoupling and order reduction, etc. In this paper
several algorithms for solving differential ...
[EN] In this work we introduce new rational-polynomial Hermite matrix expansions which allow us to obtain a new accurate and efficient method for computing the matrix cosine. This method is compared with other state-of-the-art ...
[EN] This paper presents an implementation of one of the most up-to-day algorithms proposed to compute the matrix trigonometric functions sine and cosine. The method used is based on Taylor series approximations which ...
[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 ...
The simulation in computers of the evolution of pressure and temperature inside a cavity when acoustic energy is injected results in a very stiff and high time consuming application. The split-step method used for the ...
[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 ...
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)
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 ...
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 ...
In this paper a method for computing hyperbolic matrix functions based on Hermite matrix polynomial expansions is outlined. Hermite series truncation together with Paterson-Stockmeyer method allow to compute the hyperbolic ...
Differential matrix Riccati equations (DMREs) enable to model many physical systems appearing in different branches of science, in some cases, involving very large problem sizes. In this paper, we propose an adaptive ...
In this work, we developed a parallel algorithm to speed up the resolution of differential matrix Riccati
equations using a backward differentiation formula algorithm based on a fixed-point method. The role and
use of ...
[EN] The computation of matrix trigonometric functions has received remarkable attention in
the last decades due to its usefulness in the solution of systems of second order linear
differential equations. Several ...