qd block algorithm

The block qd algorithm is studied in order to obtain some properties about the asymptotic behavior of some eigenvalues of a block tridiagonal positive definite symmetric matrix. We prove that the eigenvalues of the first block on the block diagonal of the decomposition given by the block qd algorith...

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Veröffentlicht in:Applied numerical mathematics Jg. 60; H. 12; S. 1300 - 1308
Hauptverfasser: Draux, André, Sadik, Mohamed
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.12.2010
Elsevier
Schlagworte:
Algorithms
Asymptotic properties
Block LR algorithm
Block qd algorithm
Blocking
Convergence
Decomposition
Eigenvalues
Jacobi matrix
Mathematical models
Mathematics
Matrix orthogonal polynomial
Matrix three term recurrence relation
Numerical Analysis
Block LR algorithm
Eigenvalues
Block qd algorithm
Matrix three term recurrence relation
Jacobi matrix
Matrix orthogonal polynomial
ISSN:0168-9274, 1873-5460
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Zusammenfassung:The block qd algorithm is studied in order to obtain some properties about the asymptotic behavior of some eigenvalues of a block tridiagonal positive definite symmetric matrix. We prove that the eigenvalues of the first block on the block diagonal of the decomposition given by the block qd algorithm at the different stages of this algorithm constitute strictly increasing sequences and those of the last block constitute strictly decreasing sequences. Moreover the convergence of this qd algorithm is proved under certain assumptions.
Bibliographie:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2010.05.005