Thomas Mach (Universität Potsdam)
Prekolloquium talk
Abstract: We discuss the definition of a Krylov subspace K(A,b) of dimension m. For all polynomials p of degree at most m the vector p(A)b is an element of K(A,b). We combine this with a polynomial approximation of 1/x on a subset of C (Weierstrass approximation theorem or Cayley-Hamilton theorem) to approximately or numerically solve the linear system Ax = b leading to the Lanczos and Arnoldi algorithm. If time permits we will touch on the Arnoldi-Ritz method and GMRES.
This talk will introduce PhD students and postdocs to the topic of the institute's colloquium starting at 14:00 in room 2.22.
