Iterative Block Lanczos Method for the Solution of Large Sparse Symmetric Eigenproblems.

摘要

This dissertation discusses the development,implementation,and application of an algorithm to solve the following problem: Compute accurate approximations to the r least eigenvalues of a large,sparse symmetric matrix A,where r is much less than n,the order of A. Application of common algorithms for solving general symmetric eigenproblems would require excessive computer time. The method considered is organized about a block Lanczos algorithm,which is an extension and generalization of a method originally proposed by Lanczos. Numerical examples and a listing of the computer program are included.