KrylovUnterräumen
Krylov subspaces are fundamental concepts in numerical linear algebra, particularly in the iterative solution of large sparse linear systems and eigenvalue problems. A Krylov subspace is the vector subspace spanned by the first k vectors in the sequence v, Av, A^2v, ..., A^(k-1)v, where A is a given matrix and v is a non-zero vector, often called the starting vector. These subspaces are denoted as K_k(A, v).
The significance of Krylov subspaces lies in the fact that many popular iterative methods, such as the
The dimension of K_k(A, v) is at most k. The dimension becomes stationary when the vectors v,