The algebraic eigenvalue problem
The algebraic eigenvalue problem
A Divide-and-Conquer Algorithm for the Symmetric TridiagonalEigenproblem
SIAM Journal on Matrix Analysis and Applications
Applied numerical linear algebra
Applied numerical linear algebra
The symmetric eigenvalue problem
The symmetric eigenvalue problem
A Comparison of Several Bandwidth and Profile Reduction Algorithms
ACM Transactions on Mathematical Software (TOMS)
Algorithm 508: Matrix Bandwidth and Profile Reduction [F1]
ACM Transactions on Mathematical Software (TOMS)
Algorithm 509: A Hybrid Profile Reduction Algorithm [F1]
ACM Transactions on Mathematical Software (TOMS)
Algorithm 582: The Gibbs-Poole-Stockmeyer and Gibbs-King Algorithms for Reordering Sparse Matrices
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
Multi-sweep Algorithms for the Symmetric Eigenproblem
VECPAR '98 Selected Papers and Invited Talks from the Third International Conference on Vector and Parallel Processing
Computing Approximate Eigenpairs of Symmetric Block Tridiagonal Matrices
SIAM Journal on Scientific Computing
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
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 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 or "effectively zero" (with respect to the given accuracy tolerance) elements. In the light of a recently developed block tridiagonal divide-and-conquer eigensolver [Gansterer, Ward, Muller, and Goddard, III, SIAM J. Sci. Comput. 25 (2003), pp. 65--85], for which block tridiagonalization may be needed as a preprocessing step, the algorithm also provides an option for attempting to produce at least a few very small diagonal blocks in the block tridiagonal matrix. This leads to low time complexity of the last merging operation in the block divide-and-conquer method. Numerical experiments are presented and various block tridiagonalization strategies are compared.