A study of the efficiency of iterative methods for linear problems in structural mechanics

1986 ◽  
Vol 22 (1) ◽  
pp. 209-218 ◽  
Author(s):  
A. Samuelsson ◽  
N-E. Wiberg ◽  
L. Bernspång
Keyword(s):  
Iterative Methods ◽  
Structural Mechanics ◽  
Linear Problems

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.

scholarly journals The Use of Iterative Methods in Solving Tasks of Structural Mechanics

2016 ◽  
Vol 165 ◽  
pp. 1705-1709
Author(s):  
Vladimir Kuroedov ◽  
Luka Akimov ◽  
Artem Frolov ◽  
Aleksandr Zavylov ◽  
Aleksey Savchenko
Keyword(s):  
Iterative Methods ◽  
Structural Mechanics

scholarly journals SOLUTION OF NON-LINEAR PROBLEMS OF STRUCTURAL MECHANICS BY METHOD OF STEEPEST DESCENT

2017 ◽  
Vol 13 (3) ◽  
pp. 103-111
Author(s):  
Vladilen V. Petrov
Keyword(s):  
Solid Mechanics ◽  
Nonlinear Differential Equations ◽  
Structural Mechanics ◽  
Steepest Descent ◽  
Linear Operators ◽  
Nonlinear Operators ◽  
Complex Linear ◽  
Linear Problems ◽  
Incremental Form ◽  
Method Of Steepest Descent

The algorithm of application of the method of steepest descent to the solution of problems of structural mechanics and solid mechanics, described by nonlinear differential equations. For application of this method to nonlinear operators are described by a sequence of linear operators in incremental form, unlimited and complex linear operator, in line with the idea of L. V. Kantorovich is limited to a simple linear unbounded operator.

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