Prof. Jorge Sastre
Universidad Politécnica de Valencia, Spain
Title: Beyond Paterson-Stockmeyer: Advancing Matrix Polynomial Computation
Abstarct: Since 1973, the Paterson-Stockmeyer method has been regarded as the most efficient approach for evaluating general matrix polynomials. In this plenary talk, we challenge this long-standing belief by demonstrating that newly developed methods surpass its efficiency. Furthermore, for decades, rational approximations have been considered superior to polynomial approximations in computational efficiency. However, we reveal that polynomial approximations can achieve a higher order of accuracy than state-of-the-art rational methods at the same computational cost. Through theoretical insights and practical examples, we showcase the implications of these findings for advanced matrix computations, with potential applications in scientific computing, numerical analysis, and artificial intelligence.
Bio: Dr. Jorge Sastre was Fulbright Research Scholar at New York University (NYU) in 2024. Dr. Sastre is a Full Professor at the Institute of Telecommunications and Multimedia Applications at the Universitat Politècnica de València (UPV). He holds a PhD in Applied Mathematics(Cum laude) and an M.Sc. in Telecommunication Engineering (First Class Honors), with multiple awards, including the Bankia Award and a Spanish National Award. Apart from NYU, he has been a visiting scholar at Carnegie Mellon University, UC Berkeley, Dublin City University, KTH Royal Institute of Technology, and the Monterrey Institute of Technology. In 2013, he was awarded a Spanish Ministry of Education and Science scholarship for research at Carnegie Mellon University, where he later taught in 2014.
He has directed 18 research projects, including work on matrix functions and artificial intelligence, funded by the Generalitat Valenciana and the Spanish Ministry of Economy and Competitiveness. His research focuses on matrix functions, matrix polynomials, and their applications, with over 90 publications in international journals and conferences. His key contributions to computation and applied mathematics include:
1. Developing a more efficient method for evaluating general matrix polynomials, surpassing the Paterson–Stockmeyer method, long considered the state-of-the-art.
2. Introducing a new mixed rational and polynomial approximation for matrix functions, improving efficiency in computing the matrix exponential and cosine.
3. Demonstrating that polynomial approximations (Taylor and Hermite) can outperform Padé approximations in both accuracy and computational cost.
4. Proving a theorem on matrix function expansion using non-Hermitian matrix polynomial series (Laguerre series).
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