Some Iterative Methods for Linear Operator Equations with Applications to Generalized Inverses

1977 ◽  
Vol 32 (3) ◽  
pp. 610-618 ◽  
Author(s):  
L. J. Lardy
Keyword(s):  
Linear Operator ◽  
Iterative Methods ◽  
Generalized Inverses ◽  
Operator Equations ◽  
Linear Operator Equations

scholarly journals Aggregation-iterative analogues and generalizations of projection-iterative methods

2013 ◽  
Vol 5 (1) ◽  
pp. 156-163
Author(s):  
B.A. Shuvar ◽  
A.F. Obshta ◽  
M.I. Kopach
Keyword(s):  
Linear Operator ◽  
Iterative Methods ◽  
Spectral Radius ◽  
Iterative Algorithms ◽  
Operator Equations ◽  
Convergence Conditions ◽  
Fixed Sign ◽  
Linear Operator Equations

Aggregation-iterative algorithms for linear operator equations are constructed and investigated. These algorithms cover methods of iterative aggregation and projection-iterative methods. In convergence conditions there is neither requirement for the corresponding operator of fixed sign no restriction to the spectral radius to be less than one.

M. A. Krasnosel'skii Theorem and Iterative Methods for Solving Ill-Posed Linear Problems with a Self-Adjoint Operator

2015 ◽  
Vol 15 (3) ◽  
pp. 373-389
Author(s):  
Oleg Matysik ◽  
Petr Zabreiko
Keyword(s):  
Hilbert Space ◽  
Iterative Methods ◽  
Critical Case ◽  
Adjoint Operator ◽  
Successive Approximations ◽  
Operator Equations ◽  
Ill Posed ◽  
Linear Problems ◽  
Adjoint Operators ◽  
Linear Operator Equations

AbstractThe paper deals with iterative methods for solving linear operator equations ${x = Bx + f}$ and ${Ax = f}$ with self-adjoint operators in Hilbert space X in the critical case when ${\rho (B) = 1}$ and ${0 \in \operatorname{Sp} A}$. The results obtained are based on a theorem by M. A. Krasnosel'skii on the convergence of the successive approximations, their modifications and refinements.

On nonnegative solvability of linear operator equations

1994 ◽  
Vol 18 (1) ◽  
pp. 88-108 ◽  
Author(s):  
Ruey-Jen Jang-Lewis ◽  
Harold Dean Victory
Keyword(s):  
Linear Operator ◽  
Operator Equations ◽  
Linear Operator Equations
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