Group of High Performance Scientific Computing (HiPerSC)

• Computing the Matrix Logarithm with the Romberg Integration Method, (Open Access), J. Ibáñez, J.M. Alonso, E. Defez, P. Alonso, J. Sastre, Algorithms (MDPI, ISSN 1999-4893), 16(9), 2023, 434. IF 2.3 (2022), Q3, COMPUTER SCIENCE, THEORY & METHODS 78/144, COMPUTER SCIENCE, ARTIFICIAL. INTELLIGENCE 125/192, https://doi.org/10.3390/a16090434, code.

• Accurate Approximation of the Matrix Hyperbolic Cosine Using Bernoulli Polynomials, (Open Access), J.M. Alonso, J. Ibáñez, E. Defez, F. Alvarruiz, Mathematics (MDPI, ISSN 2227-7390) Vol. 11, 2023, pp. 520. IF 2.4 (2022), Q1, MATHEMATICS, SCIE 23/329, https://doi.org/10.3390/math11030520.

• On the backward and forward error of approximations of analytic functions and applications to the computation of matrix functions, Jorge Sastre, Javier Ibáñez, Journal of Computational and Applied Mathematics, Volume 419, 2023, https://doi.org/10.1016/j.cam.2022.114706.

• Euler polynomials for the matrix exponential approximation, J.M. Alonso, J. Ibáñez, E. Defez, P. Alonso, Journal of Computational and Applied Mathematics Vol. 425, 2023, pp.115074. IF 2.4 (2022), Q1 MATHEMATICS, APPLIED – SCIE 45/267, https://doi.org/10.1016/j.cam.2023.115074, code.

• New Hermite series expansion for computing the matrix cosine (in Press and online), E. Defez, J. Ibañez, J. Peinado, P. Alonso-Jordá and J.M. Alonso, Journal of Computational and Applied Mathematics, Volume 408, July 2022, 114084, https://doi.org/10.1016/j.cam.2022.114084.

• Accurate approximation of the hyperbolic matrix cosine using Bernouilli matrix Polynomials, E. Defez, J. Ibáñez, J.M. Alonso, J.Peinado and J. Sastre, in the International Conference Mathematical Modeling in Engineering & Human Behaviour 2021,  Mathematical Modelling Conference Series at the Institute for Multidisciplinary Mathematics, Universitat Politècnica de València

• On Bernouilli matrix polynomials and matrix exponential approximation (in Press and online), E. Defez, J. Ibañez, P. Alonso-Jordá, J.M. Alonso, J. Peinado, Journal of Computational and Applied Mathematics. Volume 404, April 2022, 113207, https://doi.org 10.1016/j.cam.2020.113207

• An Improved Taylor Algorithm for Computing the Matrix Logarithm, J. Ibáñez, J. Sastre, P. Ruiz, J.M. Alonso, E. Defez ), Mathematics (MDPI, ISSN 2227-7390). Vol. 9 (17), 2021, pp. 2018.

• Efficient Evaluation of Matrix Polynomials beyond the Paterson–Stockmeyer Method (License CC BY 4.0), J. Sastre, J. Ibáñez, Mathematics 2021, 9(14), 1600; https://doi.org/10.3390/math9141600, Researchgate link: This paper provides general expressions for computing matrix polynomial approximations of order m=15 generalizing Example 5.1 from Efficient evaluation of matrix polynomials, also providing a generalization for matrix polynomial approximations of degree m=21, and 6s+3s, s=2,3, and method for evaluating general matrix polynomials of degrees m=6s, s=2,3,…, more efficiently than the Paterson-Stockmeyer method and than the general methods from Efficient evaluation of matrix polynomials.

• Advances in the Approximation of the Matrix Hyperbolic Tangent (License CC BY 4.0), J. Ibáñez, J.M. Alonso, J. Sastre, E. Defez, P.A. Alonso, Mathematics 2021, 9(11), 1219; https://doi.org/10.3390/math9111219, Researchgate Link.

• Simulation of harmonic oscillators on the lattice, M.Tung, J. Ibáñez, E. Defez, J. Sastre, Mathematical Methods in the Applied Sciences 43(14), May 2020. Researchgate Link

• Computing Matrix Trigonometric Functions with GPUs through Matlab, P. Alonso, J. Peinado, J. Ibañez, J. Sastre, E. Defez, The Journal of Supercomputing, 75, 2019, 1227–1240, doi: https://doi.org/10.1007/s11227-018-2354-1, Preprint

• On the inverse of the Caputo matrix exponential. (E. Defez, M. Tung, B. Chen-Charpentier, J.M. Alonso) Mathematics (MDPI, ISSN 2227-7390). Vol. 7 (12), 2019, pp. 1137. doi:10.3390/math7121137

• New matrix series expansions for the matrix cosine approximations, E. Defez, J. Ibáñez, P. Alonso, J.M. Alonso, Jesús Peinado and  P. Alonso-Jordá , in the International Conference Mathematical Modelling in Engineering and Human Behaviour 2019,  Mathematical Modelling Conference Series at the Institute for Multidisciplinary Mathematics, Universitat Politècnica de València,  July, 10-12, 2019, Valencia (Spain)

• An introduction to the “Group of High Performance Scientific Computing” (HiPerSC), E. Defez, J. Ibañez, J. Peinado, J. Sastre and M. Tung, in International Congress on Industrial and Applied Mathematics, ICIAM 2019, July 15th-19th 2019, Valencia (Spain).

• Computing matrix functions by matrix Bernouilli Series, E. Defez, J. Ibañez, J. Peinado, P. Alonso-Jordá and J.M. Alonso, 19th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2019, June-July 2019, Rota (Cadiz)-SPAIN.

• Fast Taylor polynomial evaluation for the matrix cosine, J. Sastre, J. Ibañez, P. Alonso, J. Peinado and E. Defez, Journal of Computational and Applied Mathematics, vol. 354 pp. 641-650, July 2019  https://doi.org/10.1016/j.cam.2018.12.041, Preprint Matlab code cosmpol.m

• Acoustic metamaterial models on the (2+1)D Schwarzschild plane, Michael M. Tung and Ewa B. Weinmüller, Journal of Computational and Applied Mathematics, vol. 346, pp. 162-170, January 2019, https://doi.org/10.1016/j.cam.2018.07.009.

• Some new Hermite matrix polynomials series expansions and their applications in hyperbolic matrix sine and cosine approximation, E. Defez, J. Ibáñez, J.Peinado, P. Alonso, J.M. Alonso and  J. Sastre, in the International Conference Mathematical Modelling in Engineering and Human Behaviour 2018,  Mathematical Modelling Conference Series at the Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, Valencia, July. 16-18, 2018.

• Fast Taylor polynomial evaluation for the matrix cosine, J. Sastre, J. Ibañez, P. Alonso, J. Peinado and E. Defez, 18th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2018, July 2018, Rota (Cadiz)-SPAIN.

• An efficient and accurate algorithm for computing the matrix cosine based on New Hermite approximations, E. Defez, J. Ibáñez, J. Peinado, J. Sastre and P. Alonso, Journal of Computational and Applied Mathematics, Volume 348, pp. 1-13. March 2019. https://doi.org/10.1016/j.cam.2018.08.047, Preprint, Matlab code cosmtayher.m.

• Boosting the computation of the matrix exponential, J. Sastre, J. Ibáñez, E. Defez, Appl. Math. Comput., 340:206-220, 2019, doi:10.1016/j.amc.2018.08.017, Preprint, Matlab code expmpol.m.

• A new efficient and accurate spline algorithm for the matrix exponential computation, Emilio Defez, Javier Ibáñez, Jorge Sastre, Jesús Peinado, Pedro Alonso. Journal of Computational and Applied Mathematics, Volume 337, pp. 354-365. August 2018. Preprint, Matlab code expmspl.m.

• Modelling acoustics on the Poincaré half-plane. Michael M. Tung. Journal of Computational and Applied Mathematics, vol.  337,  pp. 366-372,  August 2018 (online November 2017), doi:10.1016/j.cam.2017.10.037.

• A new type of Hermite matrix polynomial series, E. Defez, Michael M. Tung, Quaestiones Mathematicae, 41(2), 2018, 205–212.

• Efficient evaluation of matrix polynomials, Jorge Sastre, Linear Algebra Applications, Vol. 539, pp. 229-250, Feb. 2018, submitted Oct. 2016, published online 2017, http://dx.doi.org/10.1016/j.laa.2017.11.010, Preprint. A new family of methods to compute matrix polynomials more efficiently than Paterson-Stockmeyer method (for an early unpublished version of this work submitted on Feb. 18, 2016 to Appl. Math. Comput. see AMC-S-16-00951.pdf).

• Two algorithms for computing the matrix cosine based on new Hermite approximations, E. Defez, J. Ibáñez, J. Sastre, J. Peinado, P. Alonso, in the International Conference Mathematical Modelling in Engineering and Human Behaviour 2017,  Mathematical Modelling Conference Series at the Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, Valencia, July. 19-21, 2017.

• Two algorithms for computing the matrix cosine function, Jorge Sastre, Javier Ibáñez, Pedro Alonso Jesús Peinado, Emilio Defez. Applied Mathematics and Computation, Volume 312, pp. 66-77, November 2017, Preprint. Matlab code cosmtay.m.

• A new efficient and accurate  spline algorithm for the matrix exponential computation, E. Defez, J. Ibáñez, J. Sastre, J. Peinado, P. Alonso , in the International Conference Mathematical Modelling in Engineering and Human Behaviour 2016,  Mathematical Modelling Conference Series at the Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, Valencia, July. 18-20, 2016.

• A Fast Implementation of Matriz Trigonometrics Functions Sine and Cosine, Pedro Alonso, Jesús Peinado, Javier Ibañez. Ibáñez, Jorge Sastre, and Emilio Defez J. Peinado, P. Alonso, in the Proceedings of the 17th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2017, 4-8 July, 2017.

• Efficient and Accurate Algorithms for Computing Matrix Trigonometric Functions, P. Alonso, J. Ibáñez, J. Sastre, J. Peinado, E. Defez, Journal of Computational and Applied Mathematics, Volume 309, pp. 325-332, Jan 2017, Preprint. Matlab code costaym.m.

• Solving engineering models using hyperbolic matrix functions, Emilio Defez, Jorge Sastre, Javier Ibañez, Jesús Peinado. Applied Mathematical Modelling 40(4), Pages 2837–2844. February 2016. Preprint. Matlab code coshher.m.

• New Taylor algorithm for the matrix cosine, J. Ibáñez, J. Sastre, P. Alonso, J. Peinado, E. Defez, in the International Conference Mathematical Modelling in Engineering and Human Behaviour 2015, Mathematical Modelling Conference Series at the Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, Valencia, Sept. 9-11, 2015. Matlab code costaym.m.

• High performance computing of the matrix exponential, P. Ruiz, J. Sastre, J. Ibáñez, E. Defez, Journal of Computational and Applied Mathematics, 291, 2016, 370–379. Preprint. Matlab code exptaynsv3.m, Fortran code exptaynsv3fortran.zip.

• New scaling-squaring Taylor algorithms for computing the matrix exponential, J. Sastre, J. Ibáñez, E. Defez, P. Ruiz, SIAM Journal on Scientific Computing, 37 (1), 2015 (submitted June 21, 2009), A439-A455. Preprint. Fortran code.

• Numerical approximations of second-order matrix differential equations using higher-degree splines, E. Defez, M.M. Tung, F. Solis, J. Ibáñez, Linear and Multilinear Algebra, 64 (3), 2015, 472-489.

• Accurate and efficient matrix exponential computation, J. Sastre, J. Ibáñez, P. Ruiz, E. Defez, International Journal of Computer Mathematics, 91 (1), 2014, 97-112. Preprint. Matlab code exptaynsv2.m

• On the evaluation of matrix polynomials using several GPGPUs, Pedro Alonso, Murilo Boratto, J. Peinado, J, Ibáñez, Jorge Sastre, Tech. Report, Departament of Information Systems and Computation (DSIC), Universitat Politècnica de València.

• Solving time-invariant differential matrix Riccati equations using GPGPU computing, J. Peinado, P. Alonso, J. Ibañez, V. Hernández, M. Boratto,  Journal of Supercomputing, 70 (2), 2014, 623-636.

• A method to approximate the hyperbolic sine of a matrix, E. Defez, J. Sastre, J. Ibáñez, J. Peinado, M.M. Tung, International Journal of Complex Systems in Science, 4 (1), 2014, 41-45.

• Computing Hyperbolic Matrix Functions Using Orthogonal Matrix Polynomials, E. Defez, J. Sastre, J. Ibáñez, P.A. Ruiz, Progress in Industrial Mathematics at ECMI 2012, 2014, 403-407.
• A Rodrigues-type formula for Gegenbauer matrix polynomials, E. Defez, Applied Mathematics Letters, 26 (8), 2013, 899-903.
• Efficient computation of the matrix cosine, J. Sastre, J. Ibáñez, P. Ruiz, E. Defez, Applied Mathematics and Computation, 219, 2013, 7575-7585. Matlab code costay.m
• An adaptive Padé algorithm for the solution of time-invariant differential matrix Riccati equations, Jesús Peinado, Pedro Alonso, Javier Ibañez and Vicente Hernández in the Proceedings of the 13th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2013, 24-27 June, 2013.
• Speeding Up solving of Differential Matrix Ricatti Equations using GPGPU Computing and MATLAB, J. Peinado, J. Ibañez, E. Arias, V. Hernández, Concurrency and Computation: Practice and Experience, 24 (12), 2012, 1334-1348.

• Computing matrix functions arising in engineering models with orthogonal matrix polynomials, E. Defez, J. Sastre, J. Ibáñez, P. Ruiz, Mathematical and Computer Modelling, 57 (7-8), 2013, 1738-1743. Matlab code cosher.m

• Numerical solutions of matrix differential models using higher-order matrix splines, E. Defez, A. Hervás, J. Ibáñez, M.M. Tung, Mediterranean Journal of Mathematics, 9, 2012, 865-882.

• Efficient mixed rational and polynomial approximation of matrix functions, J. Sastre, Applied Mathematics and Computation 218 (24), 2012, 11938-11946.

• Approximating and computing nonlinear matrix differential models, E. Defez, M.M. Tung, J. Ibáñez, J. Sastre, Mathematical and Computer modelling, 55 (7-8), 2012, 2012-2022.

• Application of Laguerre matrix polynomials to the numerical inversion of Laplace transforms of matrix functions, J. Sastre, E. Defez, L. Jódar, Applied Mathematics letters, 24, 2011, 1527-1532.

• Accurate matrix exponential computation to solve coupled differential models in Engineering, J. Sastre, J. Ibáñez, E. Defez, P. Ruiz, Mathematical and Computer modelling, 54, 2011, 1835-1840. Matlab code exptayns.m

• Efficient orthogonal matrix polynomial based method for computing matrix exponential, J. Sastre, J. Ibáñez, E. Defez, P. Ruiz, Applied Mathematics and Computation, 217, 2011, 6451-6463. Matlab code dgeexfhrp.m

• Improvement on the Bound of Hermite Matrix Polynomials, E. Defez, M.M. Tung, J. Sastre, Linear Algebra And its Applications, 434, 2011, 1910-1919.

• A piecewise-linearized algorithm based on the Krylov subspace for solving stiff ODEs, J. Ibáñez, V. Hernández, P. Ruiz, E. Arias, Journal of Computational and Applied Mathematics, 235 (7), 2011, 1798-1804. Matlab and Fortran code

• Computing matrix exponential to solve coupled differential models in Engineering, J. Sastre,  J. Ibánez, E. Defez, P. Ruiz, Modelling for Addictive Behavior, Medicine and Engineering, Sept. 2010, 193-196.

• Adams-Bashforth and Adams Moulton Methods for Solving Differential Riccati Equations, J. Peinado, J Ibañez, E. Arias, V. Hernández, Computers & Mathematics with Applications, 60 (11), 2010, 3032-3045.

• Computing matrix functions solving coupled differential models, E. Defez, J. Sastre, J. Ibáñez, P. Ruiz, Mathematical and Computer modelling, 50 (5-6), 2009, 831-839.

• Solving Initial Value Problems for Ordinary Differential Equations by two approaches: BDF and piecewise-linearized methods, J. Ibáñez, V. Hernández, E. Arias, P. Ruiz, Computer Physics Communications, 180 (5), 2009, 712–723.

• Computing matrix functions solving coupled differential equations for engineering models, E. Defez, J. Sastre, J. Ibáñez, P.A. Ruiz, Modelling for Engineering and Medicine, 2008, 38-52.
• Numerical Solutions of Second-Order Matrix Models using Cubic-Matrix Splines, M.M. Tung, E. Defez, J. Sastre, Computers and Mathematics with Applications, 56, 2008, 2561-2571.

• A GMRES-based BDF Method for Solving Differential Riccati Equations, V. Hernández, J. Ibañez, J.Peinado, E. Arias, Applied Mathematics and Computation,196(2), 2008, 613-626.

• Numerical solutions of matrix differential models using cubic matrix splines II, E. Defez, A. Hervás, L. Soler, M.M. Tung, Mathematical and Computer modelling, 46, 2007, 657-669.

•  A fixed point-based BDF method for solving differential Riccati equations,  E. Arias, V. Hernández, J. Ibañez, J.Peinado, Applied Mathematics and Computation, 188, 2007, 1319-1333.

• Laguerre matrix polynomials series expansions: Theory and computer applications, J. Sastre, E. Defez, L. Jódar, Mathematical and Computer modelling, 44, 2006, 1025-1043.

• On Laguerre matrix polynomial series, J. Sastre, L. Jódar, Utilitas Mathematica 71, 2006, 109-130.

• On the asymptotics of Laguerre matrix polynomials for large x and n, J. Sastre, E. Defez, Applied Mathematics letters, 19, 2006, 721-727.

• On the asymptotics of Laguerre matrix polynomials, J. Sastre, L. Jódar, Utilitas Mathematica 70, 2006, 71-98.

• Asymptotic expressions of normalized Laguerre matrix polynomials on bounded intervals, L. Jódar, J. Sastre, Utilitas Mathematica 65, 2004, 3-31.

• Asymptotics of the modified Bessel and the incomplete Gamma matrix functions, J. Sastre, L. Jódar, Applied Mathematics Letters 16 (6), 2003, 815-820.

• Asymptotic expressions of certain type of matrix integrals, L. Jódar, J. Sastre, Applied Mathematics Letters 14 (1), 2001, 21-26.
• The growth of Laguerre matrix polynomials on bounded intervals, L. Jódar, J. Sastre, Applied Mathematics Letters 13 (8), 2000, 21-26.

• On Laguerre matrix polynomials, L. Jodar, J. Sastre, Utilitas Mathematica 53, 1998, 37-48.