Arnoldi Method

The Arnoldi method was first introduced as a *direct* algorithm
for reducing a general matrix into upper Hessenberg
form [19]. It was later discovered that this algorithm leads
to a good *iterative* technique for approximating eigenvalues of
large sparse matrices.

The algorithm works for non-Hermitian matrices. It is most useful for cases when the matrix is large but matrix-vector products are relatively inexpensive to perform. This is the situation, for example, when is large and sparse. We begin with a presentation of the basic algorithm and then describe a number of variations.

Susan Blackford 2000-11-20