Vandermonde Matrices and Convergence of Krylov Subspace Methods
Professor Rencang Li
University of Texas at Arlington
Rectangular Vandermonde matrices play a crucial role in the convergence analysis of Krylov subspace methods for linear systems and eigenvalue problems. In this talk, we will present various results on asymptotically optimal lower bounds on the condition numbers of real rectangular Vandermonde matrices and the sharpness of the existing error bounds for CG, MINRES. If time permits, we shall also analyze the convergence of GMRES on tri-diagonal Toeplitz linear systems.