Accession Number : ADA310632

Title :   An Efficient Implementation of Non Symmetric Lanczos Algorithm,

Corporate Author : CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS

Personal Author(s) : Day, David

PDF Url : ADA310632

Report Date : OCT 1995

Pagination or Media Count : 32

Abstract : Lanczos vectors computed in finite precision arithmetic by the three-term recurrence tend to lose their mutual biorthogonality. One either accepts this loss and takes more steps or re-biorthogonalizes the Lanczos vectors at each step. For the symmetric case there is a compromise approach. This compromise, known as maintaining semi-orthogonality, minimizes the cost of re-orthogonalization. This paper extends the compromise to the two-sided Lanczos algorithm, and justifies the new algorithm. The compromise is called maintaining semi-duality. An advantage of maintaining semi-duality is that the computed tridiagonal is a perturbation of a matrix that is exactly similar to the appropriate projection of the given matrix onto the computed subspaces. Another benefit is that the simple two-sided Gram-Schmidt procedure is a viable way to correct for loss of duality. Some numerical experiments show that our Lanczos code is significantly more efficient than Arnoldi's method.

Descriptors :   *ALGORITHMS, *EIGENVALUES, MATHEMATICAL MODELS, MATRICES(MATHEMATICS), EIGENVECTORS, ACCURACY, MATHEMATICAL PROGRAMMING, APPROXIMATION(MATHEMATICS), CONVERGENCE, VECTOR ANALYSIS, PERTURBATIONS, NUMERICAL METHODS AND PROCEDURES, FLOATING POINT OPERATION, ORTHOGONALITY.

Subject Categories : Numerical Mathematics
      Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE