Approximation of variational eigenvalue problems

被引：19

作者：

Solov'ev, S. I. ^{[1
]}

机构：

[1] Kazan VI Lenin State Univ, Kazan 420008, Russia

来源：

DIFFERENTIAL EQUATIONS | 2010年 / 46卷 / 07期

关键词：

Hilbert Space; Eigenvalue Problem; Bilinear Form; Spectral Problem; Subspace Versus;

D O I：

10.1134/S0012266110070104

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A variational eigenvalue problem in an infinite-dimensional Hilbert space is approximated by a problem in a finite-dimensional subspace. We analyze the convergence and accuracy of the approximate solutions. The general results are illustrated by a scheme of the finite element method with numerical integration for a one-dimensional second-order differential eigenvalue problem. For this approximation, we obtain optimal estimates for the accuracy of the approximate solutions.

引用

页码：1030 / 1041

页数：12

共 50 条

[21] Multiparameter variational eigenvalue problems with indefinite nonlinearity
Shibata, T
[J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1997, 49 (05): : 1066 - 1088
[22] Variational principle for eigenvalue problems of Hamiltonian systems
Benguria, RD
Depassier, MC
[J]. PHYSICAL REVIEW LETTERS, 1996, 77 (14) : 2847 - 2850
[23] GOULD,SH - VARIATIONAL METHODS FOR EIGENVALUE PROBLEMS
WILLIAMS, MM
[J]. CHEMISTRY IN BRITAIN, 1966, 2 (11) : 506 - &
[24] VARIATIONAL METHODS FOR NONLINEAR ELLIPTIC EIGENVALUE PROBLEMS
BROWDER, FE
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1965, 71 (01) : 176 - &
[25] DUAL VARIATIONAL-PRINCIPLES FOR EIGENVALUE PROBLEMS
AUCHMUTY, G
[J]. PROCEEDINGS OF SYMPOSIA IN PURE MATHEMATICS, 1986, 45 : 55 - 71
[26] VARIATIONAL-PRINCIPLES FOR INDEFINITE EIGENVALUE PROBLEMS
BINDING, P
YE, QA
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1995, 218 : 251 - 262
[27] On a superconvergence result for mixed approximation of eigenvalue problems
Gardini, Francesca
[J]. Numerical Mathematics and Advanced Applications, 2006, : 243 - 251
[28] Variational formulas and approximation theorems for the first eigenvalue in dimension one
Chen, M.
[J]. Science in China, Series A: Mathematics, Physics, Astronomy, 2001, 44 (04): : 409 - 418
[29] Variational formulas and approximation theorems for the first eigenvalue in dimension one
Chen, M
[J]. SCIENCE IN CHINA SERIES A-MATHEMATICS, 2001, 44 (04): : 409 - 418
[30] Variational formulas and approximation theorems for the first eigenvalue in dimension one
陈木法
[J]. Science in China,Ser.A., 2001, Ser.A.2001 (04) - 418

← 1 2 3 4 5 →