ON THE APPROXIMATION TO SOLUTIONS OF OPERATOR EQUATIONS BY THE LEAST SQUARES METHOD

被引：0
|
作者：
Gorbachuk, Myroslav L. [1 ]
Gorbachuk, Valentyna I. [1 ]
机构：
[1] Natl Acad Sci Ukraine, Inst Math, 3 Tereshchenkivska, UA-01601 Kiev, Ukraine
来源：
METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY | 2008年 / 14卷 / 03期
关键词：
Operator equation in a Hilbert space; approximate solution; least squares method; similar operator; a priori estimates; subspaces of in finitely differentiable vectors associated with a given operator and a given number seqence; entire vector of exponential type; module of continuity;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the equation Au=f, where A is a linear operator with comp act inverse in a Hilbert space. For the approximate solution u(n) of this equation by the least squares method in a coordinate system that is an orthonormal basis of eigenvectors of a self-adjoint operator B similar to A (D (A) = D (B)), we give a priori estimates for the asymptotic behavior of the expression R-n = ||Au-n - f|| as n -> 8. A relationship between the order of smallness of this expression and the degree of smoothness of the solution u with respect to the operator B (direct and converse theorems)is established
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页码：229 / 241
页数：13
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