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- Author: Hartanto Niels
- Publisher: Sudwestdeutscher Verlag Fur Hochschulschriften AG
- Year: 2011
- Pages: 112
- ISBN-10: 3838129377
- ISBN-13: 9783838129372
- Format: 15.2 x 22.9 x 0.7 cm, softcover
- Language: English
- SAVE -10% with code: EXTRA
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Description
In this thesis, spectral properties of analytic, so called m-monic operator- and matrix functions are investigated. A major focus lies on polynomials with entrywise nonnegative matrix coefficients. Crucial for the investigation of this case is the introduction of a degree reduction generalizing the well known linearization of matrix polynomials via the first companion form. This allows the development of a condition for the existence of spectral factorizations via fixpoint iterations. m-monic matrix polynomials with entrywise nonnegative coefficients such that their sum is irreducible can have eigenvalues with a symmetry similar to the rotation invariance of peripheral eigenvalues of entrywise nonnegative irreducible matrices. The analysis of this symmetry involves the well known Perron-Frobenius theory as it does in the matrix case, as well as the study of an associated infinite graph. A numerical algorithm for the computation of spectral factorizations also is given. It is based on a version of a cyclic reduction method suited for a certain type of Markov chains.
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- Author: Hartanto Niels
- Publisher: Sudwestdeutscher Verlag Fur Hochschulschriften AG
- Year: 2011
- Pages: 112
- ISBN-10: 3838129377
- ISBN-13: 9783838129372
- Format: 15.2 x 22.9 x 0.7 cm, softcover
- Language: English English
In this thesis, spectral properties of analytic, so called m-monic operator- and matrix functions are investigated. A major focus lies on polynomials with entrywise nonnegative matrix coefficients. Crucial for the investigation of this case is the introduction of a degree reduction generalizing the well known linearization of matrix polynomials via the first companion form. This allows the development of a condition for the existence of spectral factorizations via fixpoint iterations. m-monic matrix polynomials with entrywise nonnegative coefficients such that their sum is irreducible can have eigenvalues with a symmetry similar to the rotation invariance of peripheral eigenvalues of entrywise nonnegative irreducible matrices. The analysis of this symmetry involves the well known Perron-Frobenius theory as it does in the matrix case, as well as the study of an associated infinite graph. A numerical algorithm for the computation of spectral factorizations also is given. It is based on a version of a cyclic reduction method suited for a certain type of Markov chains.
Reviews