A new singular value decomposition algorithm suited to parallelization and preliminary results
ACST'06 Proceedings of the 2nd IASTED international conference on Advances in computer science and technology
Performance of a new scheme for bidiagonal singular value decomposition of large scale
PDCN'06 Proceedings of the 24th IASTED international conference on Parallel and distributed computing and networks
The design and implementation of the MRRR algorithm
ACM Transactions on Mathematical Software (TOMS)
Parallelism of double divide and conquer algorithm for singular value decomposition
PDCN'07 Proceedings of the 25th conference on Proceedings of the 25th IASTED International Multi-Conference: parallel and distributed computing and networks
Simulation of laser propagation in a plasma with a frequency wave equation
Journal of Computational Physics
Algorithm 880: A testing infrastructure for symmetric tridiagonal eigensolvers
ACM Transactions on Mathematical Software (TOMS)
A new algorithm for singular value decomposition and its parallelization
Parallel Computing
ACM Transactions on Mathematical Software (TOMS)
Parallel double divide and conquer and its evaluation on a super computer
PDCS '07 Proceedings of the 19th IASTED International Conference on Parallel and Distributed Computing and Systems
On computing the eigenvectors of a class of structured matrices
Journal of Computational and Applied Mathematics
Superquadratic convergence of DLASQ for computing matrix singular values
Journal of Computational and Applied Mathematics
Prospectus for the next LAPACK and ScaLAPACK libraries
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
MR3-SMP: A symmetric tridiagonal eigensolver for multi-core architectures
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PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume Part I
dqds with Aggressive Early Deflation
SIAM Journal on Matrix Analysis and Applications
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SIAM Journal on Scientific Computing
A shift strategy for superquadratic convergence in the dqds algorithm for singular values
Journal of Computational and Applied Mathematics
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This paper presents and analyzes a new algorithm for computing eigenvectors of symmetric tridiagonal matrices factored as LDLt, with D diagonal and L unit bidiagonal. If an eigenpair is well behaved in a certain sense with respect to the factorization, the algorithm is shown to compute an approximate eigenvector which is accurate to working precision. As a consequence, all the eigenvectors computed by the algorithm come out numerically orthogonal to each other without making use of any reorthogonalization process. The key is first running a qd-type algorithm on the factored matrix LDLt and then applying a fine-tuned version of inverse iteration especially adapted to this situation. Since the computational cost is O(n) per eigenvector for an n × n matrix, the proposed algorithm is the central step of a more ambitious algorithm which, at best (i.e., when all eigenvectors are well-conditioned), would compute all eigenvectors of an n × n symmetric tridiagonal at O(n2) cost, a great improvement over existing algorithms.