The Lanczos Algorithm for Solving Symmetric Linear Systems

摘要

The Lanczos Algorithm is becoming accepted as a powerful tool for finding the eigenvalues and eigenvectors of large sparse matrices. This dissertation considers the application of the Lanczos algorithm to the solution of large sparse symmetric systems of linear equations. We analyze the symmetric Lanczos process with various reorthogonalization methods, and present a new implementation of the algorithm, which efficiently maintains orthogonality among the Lanczos vectors. This new algorithm is discussed in detail, compared to other methods, and tested with some numerical examples. (Author)