Principles of the theory of two-dimensional infinite systems of algebraic equations

We investigate infinite systems of algebraic equations of the form 1 The numbers x ik are required quantities, and the numbers t jmik and f jm are given and real. We also consider the case where, instead of these numbers, vectors are introduced. To write down the equations under consideration in ope...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2011-10, Vol.178 (4), p.384-398
Main Author: Popov, G. Ya
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We investigate infinite systems of algebraic equations of the form 1 The numbers x ik are required quantities, and the numbers t jmik and f jm are given and real. We also consider the case where, instead of these numbers, vectors are introduced. To write down the equations under consideration in operator form, we introduce certain normed spaces and prove their completeness. In these spaces, we introduce operators with the help of which the considered equations are written. The compactness of these operators is proved. For the approximate solution of these infinite systems, we use the reduction method, according to which the upper limit in infinite sums is replaced by a finite number with increasing values. Finally, we establish the criteria of convergence of the reduction method for the considered two-dimensional infinite systems of algebraic equations.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-011-0556-7