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We present a parallel implementation of the block-tridiagonal divide-and-conquer algorithm that computes eigensolutions of symmetric block-tridiagonal matrices to reduced accuracy. In our implementation, we use mixed data/task parallelism to achieve data distribution and workload balance. Numerical tests show that our implementation is efficient, scalable… (More)

A block tridiagonalization algorithm is proposed for transforming a sparse (or "effectively" sparse) symmetric matrix into a related block tridiagonal matrix, such that the eigenvalue error remains bounded by some prescribed accuracy tolerance. It is based on a heuristic for imposing a block tridiagonal structure on matrices with a large percentage of zero… (More)

A divide-and-conquer method for computing eigenvalues and eigenvectors of a block-tridiagonal matrix with rank-one off-diagonal blocks is presented. The implications of unbalanced merging operations due to unequal block sizes are analyzed and illustrated with numerical examples. It is shown that an unfavorable order for merging blocks in the synthesis phase… (More)

A divide-and-conquer method for computing approximate eigenvalues and eigenvec-tors of a block tridiagonal matrix is presented. In contrast to a method described earlier [W. off-diagonal blocks can have arbitrary ranks. It is shown that lower rank approximations of the off-diagonal blocks as well as relaxation of deflation criteria permit the computation of… (More)

- Robert C Ward, Yihua Bai, Justin Pratt
- 2005

Many models employed to solve problems in quantum mechanics, such as electronic structure calculations, result in nonlinear eigenproblems. The solution to these problems typically involves iterative schemes requiring the solution of a large symmetric linear eigenproblem during each iteration. This paper evaluates the performance of various popular and new… (More)

Two parallel block tridiagonalization algorithms and implementations for dense real symmetric matrices are presented. Block tridiagonalization is a critical pre-processing step for the block tridiagonal divide-and-conquer algorithm for computing eigensystems and is useful for many algorithms desiring the efficiencies of block structure in matrices. For an "… (More)

- Timothy K Gates, Luis A Garcia, John W Labadie, Jim To, Valliant, P Lorenz +89 others
- 2006

For several years, Colorado State University has been documenting flow and water quality conditions in Colorado's Lower Arkansas River Valley with the goal of providing data and models that water users and managers can use to enhance both agriculture and the environment in the Valley. Extensive measurements are being made in the field, and some previously… (More)

- D H Smith, Kathleen Klein, Richard Bartholomay, Isreal Broner, G E Cardon, W M Frasier +7 others
- 2002