Multi-valued graph contraction principle with applications

Optimization ◽  
2019 ◽  
Vol 69 (7-8) ◽  
pp. 1541-1556 ◽  
Author(s):  
Adrian Petruşel ◽  
Gabriela Petruşel ◽  
Jen-Chih Yao
Keyword(s):  
Contraction Principle ◽  
Valued Graph ◽  
Graph Contraction

A note on the L-fuzzy Banach’s contraction principle

2009 ◽  
Vol 41 (5) ◽  
pp. 2399-2400 ◽  
Author(s):  
J. Martínez-Moreno ◽  
A. Roldán ◽  
C. Roldán
Keyword(s):  
Contraction Principle ◽  
Banach’S Contraction Principle

scholarly journals Convergence analysis of gradient-based iterative algorithms for a class of rectangular Sylvester matrix equations based on Banach contraction principle

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Adisorn Kittisopaporn ◽  
Pattrawut Chansangiam ◽  
Wicharn Lewkeeratiyutkul
Keyword(s):  
Spectral Radius ◽  
Matrix Equation ◽  
Iterative Algorithms ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Convergence Factor ◽  
Sylvester Matrix ◽  
Iteration Matrix ◽  
Banach Contraction ◽  
The Matrix

AbstractWe derive an iterative procedure for solving a generalized Sylvester matrix equation $AXB+CXD = E$ A X B + C X D = E , where $A,B,C,D,E$ A , B , C , D , E are conforming rectangular matrices. Our algorithm is based on gradients and hierarchical identification principle. We convert the matrix iteration process to a first-order linear difference vector equation with matrix coefficient. The Banach contraction principle reveals that the sequence of approximated solutions converges to the exact solution for any initial matrix if and only if the convergence factor belongs to an open interval. The contraction principle also gives the convergence rate and the error analysis, governed by the spectral radius of the associated iteration matrix. We obtain the fastest convergence factor so that the spectral radius of the iteration matrix is minimized. In particular, we obtain iterative algorithms for the matrix equation $AXB=C$ A X B = C , the Sylvester equation, and the Kalman–Yakubovich equation. We give numerical experiments of the proposed algorithm to illustrate its applicability, effectiveness, and efficiency.

Fuzzy double controlled metric spaces and related results

2021 ◽  
Vol 40 (5) ◽  
pp. 9977-9985
Author(s):  
Naeem Saleem ◽  
Hüseyin Işık ◽  
Salman Furqan ◽  
Choonkil Park
Keyword(s):  
Integral Equation ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Uniqueness Of Solution ◽  
Contraction Principle ◽  
Triangular Inequality ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In this paper, we introduce the concept of fuzzy double controlled metric space that can be regarded as the generalization of fuzzy b-metric space, extended fuzzy b-metric space and controlled fuzzy metric space. We use two non-comparable functions α and β in the triangular inequality as: M q ( x , z , t α ( x , y ) + s β ( y , z ) ) ≥ M q ( x , y , t ) ∗ M q ( y , z , s ) . We prove Banach contraction principle in fuzzy double controlled metric space and generalize the Banach contraction principle in aforementioned spaces. We give some examples to support our main results. An application to existence and uniqueness of solution for an integral equation is also presented in this work.

scholarly journals Efficient Distribution Analysis via Graph Contraction

1996 ◽  
Vol 24 (6) ◽  
pp. 599-620 ◽  
Author(s):  
Thomas J. Sheffler ◽  
Robert Schreiber ◽  
William Pugh ◽  
John R. Gilbert ◽  
Siddhartha Chatterjee
Keyword(s):  
Distribution Analysis ◽  
Graph Contraction ◽  
Efficient Distribution

Comments and Correction on ”U-Processes and Preference Learning” (Neural Computation Vol. 26, pp. 2896–2924, 2014)

2015 ◽  
Vol 27 (7) ◽  
pp. 1549-1553
Author(s):  
Wojciech Rejchel ◽  
Hong Li ◽  
Chuanbao Ren ◽  
Luoqing Li
Keyword(s):  
Neural Computation ◽  
Contraction Principle ◽  
Preference Learning

This note corrects an error in the proof of corollary 1 of Li et al. ( 2014 ). The original claim of the contraction principle in appendix D of Li et al. no longer holds.

scholarly journals Engineering Bi-Connected Component Overlay for Maximum-Flow Parallel Acceleration in Large Sparse Graph

2018 ◽  
Vol 36 (5) ◽  
pp. 955-962
Author(s):  
Yang Liu ◽  
Wei Wei ◽  
Heyang Xu
Keyword(s):  
Large Scale ◽  
Flow Problem ◽  
Maximum Flow ◽  
Low Complexity ◽  
Connected Components ◽  
Sparse Graphs ◽  
Fully Integrated ◽  
Flow Acceleration ◽  
Maximum Flow Problem ◽  
Graph Contraction

Network maximum flow problem is important and basic in graph theory, and one of its research directions is maximum-flow acceleration in large-scale graph. Existing acceleration strategy includes graph contraction and parallel computation, where there is still room for improvement:(1) The existing two acceleration strategies are not fully integrated, leading to their limited acceleration effect; (2) There is no sufficient support for computing multiple maximum-flow in one graph, leading to a lot of redundant computation. (3)The existing preprocessing methods need to consider node degrees and capacity constraints, resulting in high computational complexity. To address above problems, we identify the bi-connected components in a given graph and build an overlay, which can help split the maximum-flow problem into several subproblems and then solve them in parallel. The algorithm only uses the connectivity in the graph and has low complexity. The analyses and experiments on benchmark graphs indicate that the method can significantly shorten the calculation time in large sparse graphs.

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