The joint bidiagonalization process with partial reorthogonalization

Lanczos Bidiagonalization With Partial Reorthogonalization

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...

A Parallel Variant of the Gram-Schmidt Process with Reorthogonalization

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The Design of a Block Rational Lanczos Code with Partial Reorthogonalization and Implicit Restarting

We discuss the design and development of a new Fortran code EA16 for the computation of selected eigenvalues and eigenvectors of large-scale real symmetric eigenvalue problems. EA16 can be used for either the standard or the generalized eigenvalue problem. The underlying method used by EA16 is the block Lanczos method with partial reorthogonalization plus implicit restarting, combined with purg...

Bidiagonalization with Parallel Tiled Algorithms

We consider algorithms for going from a “full” matrix to a condensed “band bidiagonal” form using orthogonal transformations. We use the framework of “algorithms by tiles”. Within this framework, we study: (i) the tiled bidiagonalization algorithm BiDiag, which is a tiled version of the standard scalar bidiagonalization algorithm; and (ii) the R-bidiagonalization algorithm R-BiDiag, which is a ...