Generalized qd algorithm for block band matrices

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...

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Bibliographic Details
Published in:Numerical algorithms Vol. 61; no. 3; pp. 377 - 396
Main Authors: Draux, André, Sadik, Mohamed
Format: Journal Article
Language:English
Published: Boston Springer US 01.11.2012
Springer Nature B.V
Springer Verlag
Subjects:
Algebra
Algorithms
Computer Science
Eigenvalues
Mathematical analysis
Mathematics
Matrices (mathematics)
Numeric Computing
Numerical Analysis
Original Paper
Theory of Computation
Markov–Bernstein inequality
Eigenvalues
34L15
Block
65F15
Block band matrices
Markov–Bernstein constant
algorithm
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary: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 (Appl Numer Math 60:1300–1308, 2010 ), also remains valid in this more general case.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-012-9538-1