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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)

- Andrew Martin, Robert Ward, Frazer Bennett, Dave Clarke, Andy Harter, Steve Hodges +10 others
- 1999

A context-aware computing system is one that can deduce the state of its surroundings using input from sensors and can change its behaviour accordingly. Context-aware devices might personalise themselves to their current user, alter their functionality based on where they were being used, or take advantage of nearby computing and communications resources.… (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 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)

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)

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)

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