A Framework for Approximating Eigenpairs in Electronic Structure Computations
Computing in Science and Engineering
Block tridiagonalization of "effectively" sparse symmetric matrices
ACM Transactions on Mathematical Software (TOMS)
A parallel symmetric block-tridiagonal divide-and-conquer algorithm
ACM Transactions on Mathematical Software (TOMS)
Parallel block tridiagonalization of real symmetric matrices
Journal of Parallel and Distributed Computing
ACM Transactions on Mathematical Software (TOMS)
Parallelization of divide-and-conquer eigenvector accumulation
Euro-Par'05 Proceedings of the 11th international Euro-Par conference on Parallel Processing
Computing orthogonal decompositions of block tridiagonal or banded matrices
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I
Computing eigenvectors of block tridiagonal matrices based on twisted block factorizations
Journal of Computational and Applied Mathematics
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A divide-and-conquer method for computing approximate eigenvalues and eigenvectors of a block tridiagonal matrix is presented. In contrast to a method described earlier [W. N. Gansterer, R. C. Ward, and R. P. Muller, ACM Trans. Math. Software, 28 (2002), pp. 45--58], the 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 approximate eigenpairs with prescribed accuracy at significantly reduced computational cost compared to standard methods such as, for example, implemented in LAPACK.