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 ...
Tung, Michael Ming-Sha; Defez Candel, Emilio; Ibáñez González, Jacinto Javier; Alonso Abalos, José Miguel; Real Herráiz, Julia Irene(MDPI AG, 2022-08-09)
[EN] Differential matrix models provide an elementary blueprint for the adequate and efficient treatment of many important applications in science and engineering. In the present work, we suggest a procedure, extending our ...
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 ...
Numerical methods for solving Ordinary Differential Equations (ODEs) have received considerable attention in recent years. In this paper a piecewise-linearized algorithm based on Krylov subspaces for solving Initial Value ...
Sastre, Jorge; Ibáñez González, Jacinto Javier; Ruiz Martínez, Pedro Antonio; Defez Candel, Emilio(Taylor & Francis (Routledge): STM, Behavioural Science and Public Health Titles, 2014-01)
[EN] This work gives a new formula for the forward relative error of matrix exponential Taylor
approximation and proposes new bounds for it depending on the matrix size and the Taylor
approximation order, providing a new ...
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, ...
Alonso Abalos, José Miguel; Ibáñez González, Jacinto Javier; Defez Candel, Emilio; Alvarruiz Bermejo, Fernando(MDPI AG, 2023-02)
[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 ...
The matrix exponential plays a fundamental role in linear systems arising in engineering, mechanics and control theory. This work presents a new scaling-squaring algorithm for matrix exponential computation. It uses forward ...
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 ...
Ibáñez González, Jacinto Javier; Alonso Abalos, José Miguel; Sastre, Jorge; Defez Candel, Emilio; Alonso-Jordá, Pedro(MDPI AG, 2021-06)
[EN] In this paper, we introduce two approaches to compute the matrix hyperbolic tangent.
While one of them is based on its own definition and uses the matrix exponential, the other one is
focused on the expansion of its ...
[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 ...
Ibáñez González, Jacinto Javier; Sastre, Jorge; Ruíz Martínez, Pedro Antonio; Alonso Abalos, José Miguel; Defez Candel, Emilio(MDPI AG, 2021-09)
[EN] The most popular method for computing the matrix logarithm is a combination of the inverse scaling and squaring method in conjunction with a Pade approximation, sometimes accompanied by the Schur decomposition. In ...
[EN] Differential matrix models are an important component of many interesting applications in science and engineering. This work elaborates a procedure to approximate the solutions of special non linear fourth-order matrix ...
Differential matrix models are an essential ingredient of many important scientific and
engineering applications. In this work, we propose a procedure to represent the solutions
of first-order matrix differential equations ...
[EN] This paper presents new Taylor algorithms for the computation of the matrix exponential based on recent new matrix polynomial evaluation methods. Those methods are more efficient than the well known Paterson-Stockmeyer ...
Trigonometric matrix functions play a fundamental role in the solution of second order
differential equations. Hermite series truncation together with Paterson¿Stockmeyer
method and the double angle formula technique ...
In this paper a modification of the method proposed in [E. Defez, L. Jódar, Some applications
of Hermite matrix polynomials series expansions, Journal of Computational and Applied
Mathematics 99 (1998) 105–117] for ...
[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 ...