معرفی
Javier Perez Alvaro is an Associate Professor in the Department of Mathematical Sciences at the University of Montana, College of Humanities and Sciences. His research is centered on numerical linear algebra and matrix analysis, with applications in scientific computing and data science. He teaches courses such as Data Science Analytics, Numerical Analysis, and Linear Algebra.
Research Interests: His primary focus lies in Numerical Linear Algebra, particularly Nonlinear Eigenvalue Problems, Matrix Polynomials, Linearizations, and Conditioning Analysis. He explores the theoretical and computational aspects of polynomial and rational eigenvalue problems, with applications in mechanical systems, fluid dynamics, and photonic crystals.
The recent publications reflect a strong trend in structured linearizations, perturbation theory, and rational approximations for nonlinear eigenvalue problems. His work often involves developing and analyzing new families of linearizations (e.g., Fiedler-like, block-Kronecker) that preserve matrix structure and ensure numerical stability. The focus is on backward error analysis, eigenvector accuracy, and efficient solution methods for large-scale problems.
Advising and Grants: He actively mentors undergraduate students in research projects related to Data Science and Machine Learning, including generative modeling, deep neural networks, and tiny machine learning. He is involved in the Master of Science in Data Science program. While specific grants are not listed, his collaborative work with researchers from institutions like KU Leuven, University of Manchester, and UC Santa Barbara indicates active research funding and partnerships.
Labs and Teams: His research is conducted in collaboration with a broad network of mathematicians and computational scientists. Key collaborators include María C. Quintana, Maribel Bueno, Froilán M. Dopico, Paul Van Dooren, Karl Meerbergen, and Vanni Noferini. These collaborations span topics in structured linearizations, rational matrix functions, and numerical stability.
