Generalized qd algorithm for block band matrices

Generalized qd algorithm for block band matrices

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Article ID: iaor20126134
Volume: 61
Issue: 3
Start Page Number: 377
End Page Number: 396
Publication Date: Nov 2012
Journal: Numerical Algorithms
Authors: ,
Keywords: matrices
Abstract:

The generalized qd algorithm for block band matrices is an extension of the block qd algorithm applied to a block tridiagonal matrix. This algorithm is applied to a positive definite symmetric block band matrix. The result concerning the behavior of the eigenvalues of the first and the last diagonal block of the matrix containing the entries q (k) which was obtained in the tridiagonal case is still valid for positive definite symmetric block band matrices. The eigenvalues of the first block constitute strictly increasing sequences and those of the last block constitute strictly decreasing sequences. The theorem of convergence, given in Draux and Sadik (2010), also remains valid in this more general case.

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