Applications of the monotonicity of extremal zeros of orthogonal polynomials in interlacing and optimization problems
| Autor: | Wolfgang Erb, Ferenc Toókos |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
Associated Gegenbauer polynomials
Associated Jacobi polynomials Interlacing of zeros Monotonicity of zeros Orthogonal polynomials on the unit ball Q-Meixner-Pollaczek polynomials Gegenbauer polynomials Applied Mathematics Discrete orthogonal polynomials Mathematics::Classical Analysis and ODEs Classical orthogonal polynomials Combinatorics Computational Mathematics symbols.namesake Difference polynomials Orthogonal polynomials Wilson polynomials Hahn polynomials symbols Jacobi polynomials Mathematics |
| Zdroj: | Applied Mathematics and Computation. 217:4771-4780 |
| ISSN: | 0096-3003 |
| DOI: | 10.1016/j.amc.2010.11.032 |
| Popis: | We investigate monotonicity properties of extremal zeros of orthogonal polynomials depending on a parameter. Using a functional analysis method we prove the monotonicity of extreme zeros of associated Jacobi, associated Gegenbauer and q -Meixner–Pollaczek polynomials. We show how these results can be applied to prove interlacing of zeros of orthogonal polynomials with shifted parameters and to determine optimally localized polynomials on the unit ball. |
| Databáze: | OpenAIRE |
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