Boosting the computation of the matrix exponential

Boosting the computation of the matrix exponential, J. Sastre, J. Ibáñez, E. Defez, Appl. Math. Comput. in press, 2018, doi:10.1016/j.amc.2018.08.017, PreprintMatlab code expmpol.m.

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 method. The cost of the proposed algorithms is reduced with respect to previous algorithms based on Taylor approximations. Tests have been performed to compare the MATLAB implementations of the new algorithms to a state-of-the-art Padé algorithm for the computation of the matrix exponential, providing higher accuracy and cost performances.

First article with an application of the new matrix polynomial evaluation methods from J. Sastre, Efficient evaluation of matrix polynomials, Linear Algebra Appl. 539, (2018) 229-250. With the new matrix polynomial evaluation methods, Taylor approximation methods are more efficient than Padé approximant based methods.

Modelling acoustics on the Poincaré half-plane

Modelling acoustics on the Poincaré half-plane. Michael M. Tung. Journal of Computational and Applied Mathematics DOI10.1016/j.cam.2017.10.037

Abstract: Novel advances in the field of metamaterial research have permitted the engineering of devices with extraordinary characteristics. Here, we explore the possibilities in transformation acoustics to implement a model for the simulation of acoustic wave propagation on the Poincaré half-plane-the simplest model possessing hyperbolic geometry and also of considerable historical interest. We start off from a variational principle on the given spacetime manifold to find the design description of the model in the laboratory. After examining some significant geometrical and physical properties of the Poincaré half-plane model, we derive a general formal solution for its acoustic wave propagation. A numerical example for the evolution of the acoustic potential on a rectangular region of the Poincaré half-plane concludes this discussion.