Jorge Sastre, researcher at GTS, has presented a new algorithm that improves the efficiency of matrix polynomial evaluation, a mathematical problem with applications in fields such as control theory, engineering simulations, dynamical systems, data science, and network modelling.
The work, entitled Achieving a Two-Product Reduction over the Paterson–Stockmeyer Method for Matrix Polynomial Evaluation, was presented by researcher Jorge Sastre at the XXIX Congress on Differential Equations and Applications / XIX Congress on Applied Mathematics (CEDYA/CMA).
The study’s main contribution is a new algorithm that reduces the computational cost of matrix polynomial evaluation by two matrix multiplications compared with the Paterson–Stockmeyer method, developed in 1973 and regarded for more than five decades as the benchmark approach for this problem. This improvement is particularly relevant for applications involving the approximation of matrix functions, a fundamental tool in control theory and many areas of scientific computing and engineering. The new algorithm has the potential to optimize computations used in complex engineering simulations, dynamical systems, data analysis, network modelling, and other computationally intensive applications.
The research was funded by the Generalitat Valenciana through project CIAICO/2023/275, co-led by researchers Nuria Lloret Romero and Jorge Sastre.