Large sparse symmetric eigenvalue problems with homogeneous linear constraints: The Lanczos process with inner-outer iterations
Designing and analyzing inner-outer iteration algorithms for large sparse eigenproblems is largely an unsolved problem. The authors point out that they only touch the tip of the iceberg, and many issues still remain to be resolved. They study concrete examples of problems of this type with homogeneous linear constraints. Their goal is to compute extreme eigenvalues to certain accuracy with minimum total number of inner iteration steps. They develop two stopping criteria for the inner-outer Lanczos process and provide an analysis to explain the behavior of these two processes. A variety of numerical examples demonstrating the efficiency and accuracy of the proposed approaches is presented.
scientific article; zbMATH DE number 1443453