Convergence Estimates of Krylov Subspace Methods for the Approximation of Matrix Functions Using Tools from Potential Theory
Stefan Güttel · MIMS EPrints (University of Southampton) · 2006
This diploma thesis from 2006 reviews various definitions of matrix functions and polynomial Krylov methods for their approximation. Relations to polynomial interpolation and best approximation problems are made. The convergence behavior of Ritz values associated with Hermitian matrices is investigated. A new algorithm for the solution of the constrained energy problem with a measure supported in the complex plane is developed. This algorithm is then used to study Ritz values associated with a normal non-Hermitian matrix.