LAPACK's user's guide
A parallel algorithm for reducing symmetric banded matrices to tridiagonal form
SIAM Journal on Scientific Computing
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Banded Eigenvalue Solvers on Vector Machines
ACM Transactions on Mathematical Software (TOMS)
Reduction of a band-symmetric generalized eigenvalue problem
Communications of the ACM
A framework for symmetric band reduction
ACM Transactions on Mathematical Software (TOMS)
A framework for symmetric band reduction
ACM Transactions on Mathematical Software (TOMS)
Algorithm 807: The SBR Toolbox—software for successive band reduction
ACM Transactions on Mathematical Software (TOMS)
Communication avoiding successive band reduction
Proceedings of the 17th ACM SIGPLAN symposium on Principles and Practice of Parallel Programming
ACM Transactions on Mathematical Software (TOMS)
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In this paper we explain some of the changes that have been incorporated in the latest version of the LAPACK subroutine for reducing a symmetric banded matrix to tridiagonal form. These modifications improve the performance for larger-bandwidth problems and reduce the number of operations when accumulating the transformations onto the identity matrix, by taking advantage of the structure of the initial matrix. We show that similar modifications can be made to the LAPACK subroutines for reducing a symmetric positive definite generalized eigenvalue problem to a standard symmetric banded eigenvalue problem and for reducing a general banded matrix to bidiagonal form to facilitate the computation of the singular values of the matrix.