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m-Monic Operator- and Matrix Polynomials

m-Monic Operator- and Matrix Polynomials


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About the Book

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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Product Details
  • ISBN-13: 9783838129372
  • Publisher: Sudwestdeutscher Verlag Fur Hochschulschriften AG
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Spine Width: 7 mm
  • Width: 152 mm
  • ISBN-10: 3838129377
  • Publisher Date: 20 Oct 2011
  • Height: 229 mm
  • No of Pages: 112
  • Series Title: English
  • Weight: 227 gr


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m-Monic Operator- and Matrix Polynomials
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