
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 threeterm recurrence tend to lose their mutual biorthogonality. One either accepts this loss and takes more steps or rebiorthogonalizes the Lanczos vectors at each step. For the symmetric case there is a compromise approach. This compromise, known as maintaining semiorthogonality, minimizes the cost of reorthogonalization. This paper extends the compromise to the twosided Lanczos algorithm, and justifies the new algorithm. The compromise is called maintaining semiduality. An advantage of maintaining semiduality 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 twosided GramSchmidt 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