Analysis of the Symmetric Lanczos Process.

摘要

The Lanczos algorithm is a powerful method for finding a few eigenvalues and eigenvectors of large sparse symmetric matrices. The quantities actually computed by the Lanczos algorithm diverge completely from their theoretical counterparts. In 1971 C. Paige showed that this instability merely resulted in the computation of multiple copies of eigenpairs of the matrix. This work presents and analyzes a new way of implementing the Lanczos algorithm which prevents the computation of redundant copies of eigenpairs and costs little more than simple Lanczos itself. (Author)