- Product 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.
|Number of Pages||112|
|Country of Manufacture||India|
|Product Brand||Südwestdeutscher Verlag für Hochschulschriften|
|Product Packaging Info||Box|
|In The Box||1 Piece|
|Product First Available On ClickOnCare.com||2015-08-14 00:00:00|