The origin and nature of spurious eigenvalues in the spectral tau method

被引：24

作者：

Dawkins, PT

Dunbar, SR ^{[1
]}

Douglass, RW

机构：

[1] Univ Nebraska, Dept Math & Stat, Lincoln, NE 68588 USA

[2] Lamar Univ, Dept Math, Beaumont, TX 77710 USA

[3] Idaho Natl Engn Lab, Idaho Falls, ID 83415 USA

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 1998年 / 147卷 / 02期

关键词：

spectral methods; Chebyshev-tau method; spurious eigenvalues; generalized eigenvalue problems;

D O I：

10.1006/jcph.1998.6095

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

The Chebyshev-tau spectral method for approximating eigenvalues of boundary value problems may produce spurious eigenvalues with large positive real parts, even when all true eigenvalues of the problem are known to have negative real parts. We explain the origin and nature of the "spurious eigenvalues" in an example problem. The explanation will demonstrate that the large positive eigenvalues are an approximation of infinite eigenvalues in a nearby generalized eigenvalue problem. (C) 1998 Academic Press.

引用

页码：441 / 462

页数：22

共 50 条

[21] The modified method of fundamental solutions for exterior problems of the Helmholtz equation; spurious eigenvalues and their removals
Zhang, Li-Ping
Li, Zi-Cai
Huang, Hung-Tsai
Wei, Yimin
APPLIED NUMERICAL MATHEMATICS, 2019, 145 (236-260) : 236 - 260
[22] A Legendre spectral element method for eigenvalues in hydrodynamic stability
Hill, A. A.
Straughan, B.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2006, 193 (01) : 363 - 381
[23] ON THE TRUE AND SPURIOUS EIGENVALUES BY USING THE REAL OR THE IMAGINARY-PART OF THE METHOD OF FUNDAMENTAL SOLUTIONS
Chen, I. L.
Lee, Y. T.
Kuo, P. S.
Chen, J. T.
INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS, 2013, 10 (02)
[24] Determination of spurious eigenvalues and multiplicities of true eigenvalues in the dual multiple reciprocity method using the singular-value decomposition technique
Chen, JT
Huang, CX
Wong, FC
JOURNAL OF SOUND AND VIBRATION, 2000, 230 (02) : 203 - 219
[25] Investigation on the spurious eigenvalues of vibration plates by non-dimensional dynamic influence function method
Chen, Wen
Shi, Jisong
Chen, Lin
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2009, 33 (06) : 885 - 889
[26] Solving differential eigenproblems via the spectral Tau method
Vasconcelos, P. B.
Roman, J. E.
Matos, J. M. A.
NUMERICAL ALGORITHMS, 2023, 92 (03) : 1789 - 1811
[27] A modified spectral tau method for the calculation of the Wigner function
Hug, M
Menke, C
ENUMATH 97 - 2ND EUROPEAN CONFERENCE ON NUMERICAL MATHEMATICS AND ADVANCED APPLICATIONS, 1998, : 365 - 372
[28] Solving differential eigenproblems via the spectral Tau method
P.B. Vasconcelos
J.E. Roman
J.M.A. Matos
Numerical Algorithms, 2023, 92 : 1789 - 1811
[29] AN EFFICIENT SPECTRAL METHOD FOR THE HELMHOLTZ TRANSMISSION EIGENVALUES IN POLAR GEOMETRIES
Zhang, Jun
Fan, Xinyue
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2019, 24 (09): : 4799 - 4813
[30] A New Method of Eliminating Spurious Spectral Peak based on Array Rotation
Wang, Rentao
Chen, Xulong
Li, Bin
Ma, Ke
Gao, Jian
2013 3RD INTERNATIONAL CONFERENCE ON COMPUTER SCIENCE AND NETWORK TECHNOLOGY (ICCSNT), 2013, : 1178 - 1181

← 1 2 3 4 5 →