Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897763 | Linear Algebra and its Applications | 2018 | 15 Pages |
Abstract
We revisit the numerical stability of the two-level orthogonal Arnoldi (TOAR) method for computing an orthonormal basis of a second-order Krylov subspace associated with two given matrices. We show that the computed basis is close to a basis for a second-order Krylov subspace associated with nearby matrices, provided that the norms of the given matrices are not too large or too small. Thus, we provide conditions that guarantee the numerical stability of the TOAR method in computing orthonormal bases of second-order Krylov subspaces. We also study scaling the quadratic problem for improving the numerical stability of the TOAR procedure when the norms of the matrices are too large or too small.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Karl Meerbergen, Javier PĂ©rez,