NDLI: Twisted factorization of a banded matrix

Content Provider	Springer Nature Link
Author	Vömel, Christof Slemons, Jason
Copyright Year	2009
Abstract	The twisted factorization of a tridiagonal matrix T plays an important role in inverse iteration as featured in the MRRR algorithm. The twisted structure simplifies the computation of the eigenvector approximation and can also improve the accuracy.A tridiagonal twisted factorization is given by T=M k Δ k N k where Δ k is diagonal, M k ,N k have unit diagonals, and the k-th column of M k and the k-th row of N k correspond to the k-th column and row of the identity, that is $M_{k}e_{k}=e_{k},\;e_{k}^{t}N_{k}=e_{k}^{t}$ .This paper gives a constructive proof for the existence of the twisted factorizations of a general banded matrix A. We show that for a given twist index k, there actually are two such factorizations.We also investigate the implications on inverse iteration and discuss the role of pivoting.
Ending Page	447
Page Count	15
Starting Page	433
File Format	PDF
ISSN	00063835
e-ISSN	15729125
Journal	BIT Numerical Mathematics
Issue Number	2
Volume Number	49
Language	English
Publisher	Springer Netherlands
Publisher Date	2009-02-20
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Forward factorization Computational Mathematics and Numerical Analysis Packaged methods Block-tridiagonal matrix Numeric Computing Twisted factorization Eigenvalues, eigenvectors Mathematics Banded matrix Double factorization Backward factorization
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computer Networks and Communications Computational Mathematics Software

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