Bi-Lanczos with partial orthogonalization

Lanczos Bidiagonalization With Partial Reorthogonalization

Accurate solution of the Helmholtz equation by Lanczos orthogonalization for media with loss or gain.

The numerical scheme for solving the Helmholtz equation, based on the Lanczos orthogonalization scheme, is generalized so that it can be applied to media with space-dependent absorption or gain profiles.

The Lanczos Algorithm With Partial Reorthogonalization By Horst

The Lanczos algorithm is becoming accepted as a powerful tool for finding the eigenvalues and for solving linear systems of equations. Any practical implementation of the algorithm suffers however from roundoff errors, which usually cause the Lanczos vectors to lose their mutual orthogonality. In order to maintain some level of orthogonality, full reorthogonalization (FRO) and selective orthogo...

Recycling Bi-Lanczos Algorithms: BiCG, CGS, and BiCGSTAB

Engineering problems frequently require solving a sequence of dual linear systems. This paper introduces recycling BiCG, that recycles the Krylov subspace from one pair of linear systems to the next pair. Augmented bi-Lanczos algorithm and modified two-term recurrence are developed for using the recycle space. Recycle space is built from the approximate invariant subspace corresponding to eigen...

Bounding matrix functionals via partial global block Lanczos decomposition

Approximations of expressions of the form If := trace(W T f(A)W ), where A ∈ Rm×m is a large symmetric matrix, W ∈ Rm×k with k ≪ m, and f is a function, can be computed without evaluating f(A) by applying a few steps of the global block Lanczos method to A with initial block-vector W . This yields a partial global Lanczos decomposition of A. We show that for suitable functions f upper and lower...