scholarly journals On a general iterative method for the approximate solution of linear operator equations

1963 ◽  
Vol 17 (81) ◽  
pp. 1-1 ◽  
Author(s):  
W. V. Petryshyn
Keyword(s):  
Approximate Solution ◽  
Linear Operator ◽  
Iterative Method ◽  
Operator Equations ◽  
Linear Operator Equations ◽  
General Iterative Method

scholarly journals On the iterative solution of linear operator equations with self-adjoint operators

1972 ◽  
Vol 13 (2) ◽  
pp. 241-255 ◽  
Author(s):  
J. J. Koliha
Keyword(s):  
Hilbert Space ◽  
Approximate Solution ◽  
Linear Operator ◽  
Iterative Method ◽  
Iterative Solution ◽  
Matrix Equations ◽  
Operator Equations ◽  
Adjoint Operators ◽  
Linear Operator Equations ◽  
General Iterative Method

In this paper we deal with a linear equation Au = f in a Hilbert space using a general iterative method with a constant iterative operator for the approximate solution. The method has been studied in many papers [1, 2, 4, 9, 13, 14] and thoroughly treated by Householder [3] for matrix equations and by Petryshyn [7] for operator equations in considerably general and unified manner.

A Variant of Projection-Regularization Method for Ill-Posed Linear Operator Equations

2020 ◽  
pp. 2150008
Author(s):  
Bechouat Tahar ◽  
Boussetila Nadjib ◽  
Rebbani Faouzia
Keyword(s):  
Approximate Solution ◽  
Linear Operator ◽  
Tikhonov Regularization ◽  
Hilbert Spaces ◽  
Regularization Method ◽  
Tikhonov Regularization Method ◽  
Operator Equations ◽  
Ill Posed ◽  
Rank Approximation ◽  
Linear Operator Equations

In this paper, we report on a strategy for computing the numerical approximate solution for a class of ill-posed operator equations in Hilbert spaces: [Formula: see text]. This approach is a combination of Tikhonov regularization method and the finite rank approximation of [Formula: see text]. Finally, numerical results are given to show the effectiveness of this method.

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