Applications of the monotonicity of extremal zeros of orthogonal polynomials in interlacing and optimization problems

被引：7
|
作者：
Erb, Wolfgang [2 ]
Tookos, Ferenc [1 ]
机构：
[1] Helmholtz Ctr Munich, Inst Biomath & Biometry, D-85764 Neuherberg, Germany
[2] Univ Lubeck, Inst Math, D-23560 Lubeck, Germany
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2011年 / 217卷 / 09期
关键词：
Monotonicity of zeros; Associated Jacobi polynomials; Associated Gegenbauer polynomials; q-Meixner-Pollaczek polynomials; Interlacing of zeros; Orthogonal polynomials on the unit ball; JACOBI-POLYNOMIALS; ULTRASPHERICAL POLYNOMIALS; INEQUALITIES;
D O I：
10.1016/j.amc.2010.11.032
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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. (C) 2010 Elsevier Inc. All rights reserved.
引用
收藏
页码：4771 / 4780
页数：10
相关论文
共 50 条
  • [31] Monotonicity of zeros of Laguerre polynomials
    Dimitrov, Dimitar K.
    Rafaeli, Fernando R.
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 233 (03) : 699 - 702
  • [32] Monotonicity of zeros of Jacobi polynomials
    Dimitrov, Dimitar K.
    Rafaeli, Fernando R.
    JOURNAL OF APPROXIMATION THEORY, 2007, 149 (01) : 15 - 29
  • [33] Interlacing and bounds of zeros of quasi-orthogonal little q-Jacobi polynomials
    Kar, Pinaki Prasad
    Gochhayat, Priyabrat
    NUMERICAL ALGORITHMS, 2023, 93 (03) : 1157 - 1170
  • [34] Interlacing and bounds of zeros of quasi-orthogonal little q-Jacobi polynomials
    Pinaki Prasad Kar
    Priyabrat Gochhayat
    Numerical Algorithms, 2023, 93 : 1157 - 1170
  • [35] A note on monotonicity of zeros of generalized Hermite-Sobolev-type orthogonal polynomials
    Marcellan, Francisco
    Rafaeli, Fernando R.
    INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2010, 21 (11) : 831 - 838
  • [36] Interlacing of the zeros of Jacobi polynomials with different parameters
    Kathy Driver
    Kerstin Jordaan
    Norbert Mbuyi
    Numerical Algorithms, 2008, 49 : 143 - 152
  • [37] Interlacing Property of Zeros of Shifted Jacobi Polynomials
    Cvetkovic, Aleksandar S.
    APPROXIMATION AND COMPUTATION: IN HONOR OF GRADIMIR V. MILOVANOVIC, 2011, 42 : 97 - 101
  • [38] New proofs of interlacing of zeros of Eulerian polynomials
    Chow, Chak-On
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2022, 510 (02)
  • [39] Zeros of orthogonal polynomials
    Badkov, V. M.
    TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2005, 11 (02): : 30 - 46
  • [40] Interlacing of the zeros of Jacobi polynomials with different parameters
    Driver, Kathy
    Jordaan, Kerstin
    Mbuyi, Norbert
    NUMERICAL ALGORITHMS, 2008, 49 (1-4) : 143 - 152
12345