Arnoldi Iteration

This is the third post in my series on Krylov subspaces. The first post is here and the second one is here. The Lanczos Algorithm In this post we cover the Lanczos algorithm that gives you eigenvalues and eigenvectors of symmetric matrices. The Lanczos algorithm is named after Cornelius Lanczos, who was quite influential with his research. He also proposed an interpolation method and a method to approximate the gamma function.

This is the second post in my series on Krylov subspaces. The first post is here and the third one is here. Arnoldi Iterations Arnoldi iterations is an algorithm to find eigenvalues and eigenvectors of general matrices. The algorithm constructs orthonormal bases of suitable Krylov subspaces and extracts the eigendata from the basis representation. The method is named after the American engineer Walter Edwin Arnoldi and was published in 1951 [1].