Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4598578 | Linear Algebra and its Applications | 2016 | 13 Pages |
Abstract
The extended Krylov subspace method is known to be very efficient in many cases in which one wants to approximate the action of a matrix function f(A)f(A) on a vector b, in particular when f belongs to the class of Laplace–Stieltjes functions. We prove that the Euclidean norm of the error decreases strictly monotonically in this situation when A is Hermitian positive definite. Similar results are known for the (polynomial) Lanczos method for f(A)bf(A)b, and we demonstrate how the techniques of proof used in the polynomial Krylov case can be transferred to the extended Krylov case.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Marcel Schweitzer,