Approximate solution of linear operator equations in Hilbert space by the method of least squares. II

1967 ◽  
Vol 7 (3) ◽  
pp. 1-29 ◽  
Author(s):  
V.V Ivanov ◽  
V.Yu Kudrinskii
Keyword(s):  
Hilbert Space ◽  
Approximate Solution ◽  
Linear Operator ◽  
Least Squares ◽  
Method Of Least Squares ◽  
Operator Equations ◽  
Linear Operator Equations

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 fixed point method to solve linear operator equations involving self-adjoint operators in Hilbert space

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3249-3251
Author(s):  
Mohammad Khan ◽  
Dinu Teodorescu
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Adjoint Operator ◽  
Fixed Point Method ◽  
Operator Equations ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Adjoint Operators ◽  
Invertible Matrices ◽  
Linear Operator Equations

In this paper we provide existence and uniqueness results for linear operator equations of the form (I+Am) x = f , where A is a self-adjoint operator in Hilbert space. Some applications to the study of invertible matrices are also presented.

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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