An extended set of FORTRAN basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
A parallel algorithm for reducing symmetric banded matrices to tridiagonal form
SIAM Journal on Scientific Computing
Basic Linear Algebra Subprograms for Fortran Usage
ACM Transactions on Mathematical Software (TOMS)
Using Pentangular Factorizations for the Reduction to Banded Form
Euro-Par '99 Proceedings of the 5th International Euro-Par Conference on Parallel Processing
Cache efficient bidiagonalization using BLAS 2.5 operators
ACM Transactions on Mathematical Software (TOMS)
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A parallel algorithm for reducing banded matrices to bidiagonal form is presented. In contrast to the rotation-based ''standard approach'', our algorithm is based on Householder transforms, therefore exhibiting considerably higher data locality (BLAS level 2 instead of level 1). The update of the transformation matrices which involves the vast majority of the operations can even be blocked to allow the use of level 3 BLAS. Thus, our algorithm will outperform the standard method on a serial computer with a distinct memory hierarchy. In addition, the algorithm can be efficiently implemented in a distributed memory environment, as is demonstrated by numerical results on the Intel Paragon.