A convergent simplicial algorithm with ω-subdivision and ω-bisection strategies

2011 ◽  
Vol 52 (3) ◽  
pp. 371-390 ◽  
Author(s):  
Takahito Kuno ◽  
Paul E. K. Buckland
Keyword(s):  
Simplicial Algorithm

Triangulating between parallel splitting contours using a simplicial algorithm

1991 ◽  
Author(s):  
Rick Miranda ◽  
Thomas O. McCracken ◽  
Chris Fedde
Keyword(s):  
Simplicial Algorithm ◽  
Parallel Splitting

Optimized PSO algorithm based on the simplicial algorithm of fixed point theory

2020 ◽  
Vol 50 (7) ◽  
pp. 2009-2024 ◽  
Author(s):  
Minglun Ren ◽  
Xiaodi Huang ◽  
Xiaoxi Zhu ◽  
Liangjia Shao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Pso Algorithm ◽  
Point Theory ◽  
Simplicial Algorithm

scholarly journals A Simplicial Algorithm for the Nonlinear Stationary Point Problem on an Unbounded Polyhedron

1991 ◽  
Vol 1 (2) ◽  
pp. 151-165 ◽  
Author(s):  
Y. Dai ◽  
G. van der Laan ◽  
A. J. J. Talman ◽  
Y. Yamamoto
Keyword(s):  
Stationary Point ◽  
Point Problem ◽  
Simplicial Algorithm

Fixed Points-Contractive Functions

2001 ◽  
Author(s):  
Krzysztof A. Sikorski
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Research Area ◽  
Banach Fixed Point Theorem ◽  
Homotopy Methods ◽  
Simplicial Algorithm ◽  
Intensive Research ◽  
Fixed Point Computation

Fixed point computation has been an intensive research area since 1967 when Scarf introduced simplicial algorithm to approximate fixed points. Several algorithms have been invented since then, including restart and homotopy methods. Most of these were designed to approximate fixed points of general maps and used the residual error criterion. In this chapter we consider the absolute and/or relative error criteria for contractive univariate and multivariate functions. The departure of our analysis is the classical Banach fixed point theorem. Namely, we consider a function f : D →D, where D is a closed subset of a Banach space B. We assume that f is contractive with a factor q < 1, i.e., . . . ||f(x) – f(y)|| ≤ q ||x-y||, for all x,y ∈ D. Then, there exists a unique ∝ = ∝ (f) ∈ D such that ∝ is a fixed point of f, ∝ = f (∝)

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