AN ITERATIVE METHOD OF GENERALIZED SEPARATION OF VARIABLES FOR SOLVING LINEAR OPERATOR EQUATIONS

被引：0
作者：
Biletskyy, V. M. [1 ]
机构：
[1] Ivan Franko Natl Univ Lviv, 1 Univ Str, UA-79000 Lvov, Ukraine
来源：
JOURNAL OF NUMERICAL AND APPLIED MATHEMATICS | 2010年 / 1卷 / 100期
关键词：
Tensor-product representation; Generalized separation of variables; Iterative algorithms; Linear operator equation;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
An iterative method of generalized variables separation is proposed for solving linear operator equations in a Hilbert space which is a tensor product of n Hilbert spaces. A solution of an equation is represented as a series where each term is a tensor product of n elements of respective spaces. Such a way of problem solving allows to decrease a computational complexity of a problem. The method convergence is proven and numerical results are given.
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页码：2 / 9
页数：8
相关论文
共 21 条
[1]  
Balyash Y., 1986, EQUATIONS APPL MODEL, V2, P23
[2]  
Balyash Y., 1985, WAVES DIFFRACTION, V1, P122
[3]  
Balyash Yu. G., 1989, The 1989 URSI International Symposium on Electromagetic Theory, P650
[4]  
Biletskyy V, 2007, DIPED 2007: DIRECT AND INVERSE PROBLEMS OF ELECTROMAGNETIC AND ACOUSTIC WAVE THEORY, P94, DOI 10.1109/DIPED.2007.4373583
[5]   A multilinear singular value decomposition [J].
De Lathauwer, L ;
De Moor, B ;
Vandewalle, J .
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2000, 21 (04) :1253-1278
[6]   On the best rank-1 and rank-(R1,R2,...,RN) approximation of higher-order tensors [J].
De Lathauwer, L ;
De Moor, B ;
Vandewalle, J .
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2000, 21 (04) :1324-1342
[7]   Hierarchical tensor-product approximation to the inverse and related operators for high-dimensional elliptic problems [J].
Gavrilyuk, IP ;
Hackbusch, W ;
Khoromskij, BN .
COMPUTING, 2005, 74 (02) :131-157
[8]   Hierarchical Kronecker tensor-product approximations [J].
Hackbusch, W. ;
Khoromskij, B.N. ;
Tyrtyshnikov, E.E. .
Journal of Numerical Mathematics, 2005, 13 (02) :119-156
[9]  
Hackbusch W., 2008, 782008 MPI MIS LEIPZ
[10]   Tensor-product approximation to operators and functions in high dimensions [J].
Hackbusch, Wolfgang ;
Khoromskij, Boris N. .
JOURNAL OF COMPLEXITY, 2007, 23 (4-6) :697-714
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