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Treffer: Aspects of nonnormality for iterative methods

Title:
Aspects of nonnormality for iterative methods
Authors:
Marko Huhtanen
Source:
Linear Algebra and its Applications. 394:119-144
Publisher Information:
Elsevier BV, 2005.
Publication Year:
2005
Subject Terms:
Binormal matrix, Involution, Iterative numerical methods for linear systems, Measure of nonnormality, Iterative methods, Numerical computation of matrix norms, conditioning, scaling, Ritz values, algorithms, 01 natural sciences, iterative methods for linear systems, Computational methods for sparse matrices, binormal matrix, nonnormal matrix, involution, Discrete Mathematics and Combinatorics, Hermitian, skew-Hermitian, and related matrices, unitary orbit, 0101 mathematics, Unitary orbit, circulant matrix, Numerical Analysis, Algebra and Number Theory, minimal normal polynomial, Polynomially normal operator, polynomially normal operator, measure of nonnormality, Geometry and Topology, Nonnormal matrix
Document Type:
Fachzeitschrift Article
File Description:
application/xml
Language:
English
ISSN:
0024-3795
DOI:
10.1016/j.laa.2004.06.026
Access URL:
https://zbmath.org/2137776
https://doi.org/10.1016/j.laa.2004.06.026
https://www.sciencedirect.com/science/article/abs/pii/S0024379504003027
https://core.ac.uk/display/81201208
https://research.aalto.fi/en/publications/publication(b0a19586-ebbc-440a-970b-446ed7ed55dc)/export.html
https://research.aalto.fi/en/publications/aspects-of-nonnormality-for-iterative-methods(b0a19586-ebbc-440a-970b-446ed7ed55dc).html
https://www.sciencedirect.com/science/article/pii/S0024379504003027
Rights:
Elsevier Non-Commercial
Accession Number:
edsair.doi.dedup.....d15bbf1fa8eebe549629d25ba400e8f7
Database:
OpenAIRE

Weitere Informationen

The paper deals with the study of various aspects of nonnormality of matrices arising from the existence of some algorithms. First, the binormal matrices are introduced and the dimension of the set of binormal matrices is computed. A related circulant matrix structure is highlighted, and the polynomial normality for matrices are defined. The author discusses the solution of linear systems involving nonnormal matrices. It is proved that a linear system involving a binormal matrix can be solved by executing an optimal 3-term recurrence for normal matrices. Since polynomial normality of particular degree remains invariant under unitary similarity transformations, the unitary orbit of binormal matrices and polynomially normal matrices of moderate degree, are considered. Measures of nonnormality related to iterative methods are discussed and three algorithms for computing the minimal normal polynomial of a matrix are presented.