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Jianlin Xia, Professor

Department of Mathematics

Purdue University

Abstract: In this talk, we will present fast and superfast methods for solving some important dense and sparse eigenvalue problems. We take advantage of various types of structures in divide-and-conquer strategies, contour-integral methods, bisection, etc. Accelerations of the eigenvalue solutions are made via randomization, fast multipole strategies, multi-shifted factorization, fast eigenvalue count, etc. For certain cases, nearly linear complexity can be achieved for the entire eigenvalue decomposition. The accuracy and stability behaviors will be justified. The fast eigenvalue solutions provide ways to tackle some major computational challenges in traditional numerical computations, especially PDE solutions.