A fully parallel algorithm for the symmetric eigenvalue problem
SIAM Journal on Scientific and Statistical Computing
On the spectral decomposition of Hermitian matrices modified by low rank perturbations
SIAM Journal on Matrix Analysis and Applications
On the orthogonality of eigenvectors computed by divide-and-conquer techniques
SIAM Journal on Numerical Analysis
Error analysis of update methods for the symmetric eigenvalue problem
SIAM Journal on Matrix Analysis and Applications
A Stable and Efficient Algorithm for the Rank-One Modification of the Symmetric Eigenproblem
SIAM Journal on Matrix Analysis and Applications
A Divide-and-Conquer Algorithm for the Symmetric TridiagonalEigenproblem
SIAM Journal on Matrix Analysis and Applications
Matrix computations (3rd ed.)
Applied numerical linear algebra
Applied numerical linear algebra
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
SIAM Journal on Scientific Computing
Solving secular equations stably and efficiently
Solving secular equations stably and efficiently
A Serial Implementation of Cuppen''s Divide and Conquer Algorithm
A Serial Implementation of Cuppen''s Divide and Conquer Algorithm
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)
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 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 of the algorithm may lead to a significant increase of the arithmetic complexity. A strategy to determine a good merging order that is at least close to optimal in all cases is given. The method has been implemented and applied to test problems from a quantum chemistry application.