GENERALIZED CHARACTERISTIC POLYNOMIALS AND GAUSSIAN CUBATURE RULES

被引：4

作者：

Xu, Yuan ^{[1
]}

机构：

[1] Univ Oregon, Dept Math, Eugene, OR 97403 USA

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2015年 / 36卷 / 03期

关键词：

generalized characteristic polynomials; orthogonal polynomials; Toeplitz matrix; Gaussian cubature rule; VARIABLES; MATRICES;

D O I：

10.1137/140972810

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a family of near banded Toeplitz matrices, generalized characteristic polynomials are shown to be orthogonal polynomials of two variables, which include the Chebyshev polynomials of the second kind on the deltoid as a special case. These orthogonal polynomials possess a maximal number of real common zeros, which generate a family of Gaussian cubature rules in two variables.

引用

页码：1129 / 1142

页数：14

共 50 条

[21] Cubature Formula for Bivariate Generalized Chebyshev Koornwinder's Type Polynomials
AlMheidat, Maalee
AyyalSalman, Khaldoun
AlQudah, Mohammad
INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017), 2018, 1978
[22] Extended homogeneous bivariate orthogonal polynomials: symbolic and numerical Gaussian cubature formula
Abouir, Jilali
Benouahmane, Brahim
NUMERICAL ALGORITHMS, 2024, 97 (04) : 1535 - 1561
[23] Generalized Characteristic Polynomials of Join Graphs and Their Applications
Lu, Pengli
Gao, Ke
Yang, Yang
DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2017, 2017
[24] CUBATURE FORMULAE FOR THE GAUSSIAN WEIGHT. SOME OLD AND NEW RULES.
Orive, Ramon
Santos-Leon, Juan C.
Spalevic, Miodrag M.
ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS, 2020, 53 : 426 - 438
[25] On the construction of graphs determined by their generalized characteristic polynomials
Mao, Lihuan
Wang, Wei
LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 485 : 454 - 466
[26] Quick Black Box Variational Inference Using Gaussian Cubature Integration Rules
Meller, Michal
2021 IEEE RADAR CONFERENCE (RADARCONF21): RADAR ON THE MOVE, 2021,
[27] Characteristic polynomials of nonnegative real square matrices and generalized clique polynomials
Lavallee, Sylvain
LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 433 (01) : 118 - 126
[28] EFFICIENT SYMMETRICAL CUBATURE RULES FOR COMPLETE POLYNOMIALS OF HIGH DEGREE OVER THE UNIT CUBE
DUNAVANT, DA
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1986, 23 (03) : 397 - 407
[29] Generalized Gaussian quadrature rules on arbitrary polygons
Mousavi, S. E.
Xiao, H.
Sukumar, N.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2010, 82 (01) : 99 - 113
[30] EFFICIENT CUBATURE RULES
Van Zandt, James R.
ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS, 2019, 51 : 219 - 239

← 1 2 3 4 5 →