On global convergence of iterative methods

1982 ◽  
pp. 1-19 ◽  
Author(s):  
O. Axelsson
Keyword(s):  
Global Convergence ◽  
Iterative Methods

scholarly journals The “global” convergence of Broyden-like methods with suitable line search

1986 ◽  
Vol 28 (1) ◽  
pp. 75-92 ◽  
Author(s):  
Anderas Griewank
Keyword(s):  
Global Convergence ◽  
Iterative Methods ◽  
Level Set ◽  
Superlinear Convergence ◽  
Line Search ◽  
Divided Difference ◽  
Inverse Function ◽  
System Of Nonlinear Equations ◽  
Derivative Free ◽  
Quasi Newton

Iterative methods for solving a square system of nonlinear equations g(x) = 0 often require that the sum of squares residual γ (x) ≡ ½∥g(x)∥2 be reduced at each step. Since the gradient of γ depends on the Jacobian ∇g, this stabilization strategy is not easily implemented if only approximations Bk to ∇g are available. Therefore most quasi-Newton algorithms either include special updating steps or reset Bk to a divided difference estimate of ∇g whenever no satisfactory progress is made. Here the need for such back-up devices is avoided by a derivative-free line search in the range of g. Assuming that the Bk are generated from an rbitrary B0 by fixed scale updates, we establish superlinear convergence from within any compact level set of γ on which g has a differentiable inverse function g−1.

scholarly journals Modified Dai-Yuan iterative scheme for Nonlinear Systems and its Application

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Mohammed Yusuf Waziri ◽  
Kabiru Ahmed ◽  
Abubakar Sani Halilu ◽  
Aliyu Mohammed Awwal
Keyword(s):  
Nonlinear Systems ◽  
Global Convergence ◽  
Iterative Methods ◽  
Nonsmooth Optimization ◽  
Projection Method ◽  
Numerical Experiments ◽  
Iterative Scheme ◽  
Search Direction ◽  
Derivative Free ◽  
Convergence Of The Scheme

<p style='text-indent:20px;'>By exploiting the idea employed in the spectral Dai-Yuan method by Xue et al. [IEICE Trans. Inf. Syst. 101 (12)2984-2990 (2018)] and the approach applied in the modified Hager-Zhang scheme for nonsmooth optimization [PLos ONE 11(10): e0164289 (2016)], we develop a Dai-Yuan type iterative scheme for convex constrained nonlinear monotone system. The scheme's algorithm is obtained by combining its search direction with the projection method [Kluwer Academic Publishers, pp. 355-369(1998)]. One of the new scheme's attribute is that it is derivative-free, which makes it ideal for solving non-smooth problems. Furthermore, we demonstrate the method's application in image de-blurring problems by comparing its performance with a recent effective method. By employing mild assumptions, global convergence of the scheme is determined and results of some numerical experiments show the method to be favorable compared to some recent iterative methods.</p>

Comparison of Direct and Iterative Methods for Model Updating of a Curved Cable-stayed Bridge Using Experimental Modal Data

2016 ◽  
Vol 106 (8) ◽  
pp. 538-545 ◽  
Author(s):  
Guanzhe Fa ◽  
Enrico Mazzarolo ◽  
Leqia He ◽  
Bruno Briseghella ◽  
Luigi Fenu ◽  
...  
Keyword(s):  
Iterative Methods ◽  
Model Updating ◽  
Modal Data ◽  
Cable Stayed Bridge
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