Two Taylor Algorithms for Computing the Action of the Matrix Exponential on a Vector

The action of the matrix exponential on a vector eAtv, A∈Cn×n, v∈Cn, appears in problems that arise mathematics, physics, and engineering, such as solution systems linear ordinary differential equations with constant coefficients. Nowadays, several state-of-the-art approximations are available for estimating this type action. In work, two Taylor algorithms proposed computing eAv, which make use scaling recovering technique based backward or forward error analysis. A battery highly heterogeneous test matrices has been used different experiments performed to compare numerical computational properties these algorithms, implemented MATLAB language. general, both them improve those already existing literature, terms accuracy response time. Moreover, high-performance version is able take advantage power GPU platform developed, making it possible tackle high dimension at an execution time significantly reduced.