ACCURATE FACTORIZATION AND EIGENVALUE ALGORITHMS FOR SYMMETRIC DSTU AND TSC MATRICES.

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Bibliographic Details
Title:	ACCURATE FACTORIZATION AND EIGENVALUE ALGORITHMS FOR SYMMETRIC DSTU AND TSC MATRICES.
Authors:	Pelaez, Maria Jose¹ mpelaez@math.uc3m.es, Moro, Julio¹ jmoro@math.uc3m.es
Source:	SIAM Journal on Matrix Analysis & Applications. 2006, Vol. 28 Issue 4, p1173-1198. 26p. 4 Charts, 1 Graph.
Subjects:	Factorization, Factorization of operators, Eigenvalues, Matrices (Mathematics), Symmetric functions, Symmetric matrices
Abstract:	Two algorithms are presented which compute, with small componentwise relative error, a block LDLT factorization of symmetric matrices belonging to two classes of matrices: diagonally scaled totally unimodular (DSTU) and total signed compound (TSC) matrices. This accuracy is achieved by taking advantage of some special properties of such structures in order to avoid subtractions throughout the factorization process. Once an accurate block LDLT decomposition is available, it is proved that one can easily obtain an accurate symmetric rank-revealing decomposition, which is the starting point for algorithms computing with high relative accuracy the eigenvalues and eigenvectors of arbitrary, possibly indefinite, symmetric matrices. This proves that eigenvalues and eigenvectors of symmetric DSTU and TSC matrices can be computed with high relative accuracy. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	Two algorithms are presented which compute, with small componentwise relative error, a block LDLT factorization of symmetric matrices belonging to two classes of matrices: diagonally scaled totally unimodular (DSTU) and total signed compound (TSC) matrices. This accuracy is achieved by taking advantage of some special properties of such structures in order to avoid subtractions throughout the factorization process. Once an accurate block LDLT decomposition is available, it is proved that one can easily obtain an accurate symmetric rank-revealing decomposition, which is the starting point for algorithms computing with high relative accuracy the eigenvalues and eigenvectors of arbitrary, possibly indefinite, symmetric matrices. This proves that eigenvalues and eigenvectors of symmetric DSTU and TSC matrices can be computed with high relative accuracy. [ABSTRACT FROM AUTHOR]
ISSN:	08954798
DOI:	10.1137/050631537