What is ... a Krylov space? | Thomas Mach (UP)

What is ... a Krylov subspace?

Thomas Mach revives the introductory lectures to bring everyone to level with key concepts of colloquium talks, the What-is-…-? lectures. This talk introduces key concepts of Silvia Gazolla's talk on Krylov Methods for Solving Inverse Problems.

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.

Everyone is cordially invited!