The lanczos algorithm for solving symmetric linear systems
Horst D. Simon · 1982
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. ^^*Research sponsored by Office of Naval Research Contract N00014-76-C-0013.