{"product_id":"m-monic-operator-and-matrix-polynomials-spectral-properties-factorizations-and-companion-forms-von-niels-hartanto","title":"m-Monic Operator- and Matrix Polynomials","description":"\u003cp\u003eIn 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.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783838129372\"\u003e\u003ch3\u003eSpectral Properties, Factorizations and Companion Forms\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783838129372","offer_id":39441281712221,"sku":"9783838129372","price":53.9,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/34448285-1e0d-4505-a63b-99f21423e21a.jpg?v=1776315991","url":"https:\/\/shop.autorenwelt.de\/products\/m-monic-operator-and-matrix-polynomials-spectral-properties-factorizations-and-companion-forms-von-niels-hartanto","provider":"Autorenwelt Shop","version":"1.0","type":"link"}