Maximal Stationary Iterative Methods for the Solution of Operator Equations

1974 ◽  
Vol 11 (5) ◽  
pp. 934-949 ◽  
Author(s):  
H. Wozniakowski
Keyword(s):  
Iterative Methods ◽  
Operator Equations ◽  
Stationary Iterative Methods

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.

Sparse Tiling for Stationary Iterative Methods

2004 ◽  
Vol 18 (1) ◽  
pp. 95-113 ◽  
Author(s):  
Michelle Mills Strout ◽  
Larry Carter ◽  
Jeanne Ferrante ◽  
Barbara Kreaseck
Keyword(s):  
Iterative Methods ◽  
Stationary Iterative Methods
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