Arnoldi Method

The Arnoldi process is a technique for approximating a few eigenvalues and corresponding eigenvectors of a general $n\times n$ matrix. It is most appropriate for large structured matrices A, where structure means that a matrix-vector product ${\bf A}{\bf v} = {\bf w}$ requires $O \left(n \right)$rather than the usual $O \left(n^2 \right)$ floating point operations. The ARPACK library consisting of FORTRAN programs is available at the WWW site: ftp://ftp.caam.rice.edu/pub/software/ARPACK.