On fixed-point implementation of symmetric matrix inversion

2015 ◽  
Author(s):  
Carl Ingemarsson ◽  
Oscar Gustafsson
Keyword(s):  
Fixed Point ◽  
Symmetric Matrix ◽  
Matrix Inversion

scholarly journals On the Positive Definite Solutions of a Nonlinear Matrix Equation

2013 ◽  
Vol 380-384 ◽  
pp. 1434-1438
Author(s):  
Ming Hui Wang ◽  
Chun Yan Liang ◽  
Shan Rui Hu
Keyword(s):  
Fixed Point ◽  
Matrix Equation ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Positive Definite ◽  
Matrix Inversion ◽  
Nonlinear Matrix Equation ◽  
Nonlinear Matrix

In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case are discussed. An algorithm that avoids matrix inversion with the case is proposed.

scholarly journals Linear program fixed-point representation

MATEMATIKA ◽  
2017 ◽  
Vol 33 (1) ◽  
pp. 55
Author(s):  
Jalaluddin Morris Abdullah
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Symmetric Matrix ◽  
Fixed Point Problem ◽  
Linear Program ◽  
Point Problem ◽  
Central Elements ◽  
Point Representation ◽  
Primal And Dual Problems ◽  
Primal And Dual

From a linear program and its asymmetric dual, invariant primal and dual problems are constructed. Regular mappings are defined between the solution spaces of the original and invariant problems. The notion of centrality is introduced and subsets of regular mappings are shown to be inversely related surjections of central elements, thus representing the original problems as invariant problems. A fixed-point problem involving an idempotent symmetric matrix is constructed from the invariant problems and the notion of centrality carried over to it; the non-negative central fixed-points are shown to map one-to-one to the central solutions to the invariant problems, thus representing the invariant problems as a fixed-point problem and, by transitivity, the original problems as a fixed-point problem.

scholarly journals Binary Symmetric Matrix Inversion Through Local Complementation

2012 ◽  
Vol 116 (1-4) ◽  
pp. 15-23 ◽  
Author(s):  
Robert Brijder ◽  
Hendrik Jan Hoogeboom
Keyword(s):  
Symmetric Matrix ◽  
Matrix Inversion ◽  
Local Complementation

scholarly journals Inverse multiparameter eigenvalue problems for matrices II

1986 ◽  
Vol 29 (3) ◽  
pp. 343-348 ◽  
Author(s):  
Patrick J. Browne ◽  
B. D. Sleeman
Keyword(s):  
Fixed Point ◽  
Eigenvalue Problems ◽  
Symmetric Matrix ◽  
Sufficient Conditions ◽  
Degree Theory ◽  
Main Tool ◽  
Real Numbers ◽  
Inverse Eigenvalue Problems ◽  
Inverse Eigenvalue ◽  
The One

This is a sequel to our previous paper [4] where we initiated a study of inverse eigenvalue problems for matrices in the multiparameter setting. The one parameter version of the problem under consideration asks for conditions on a given n × n symmetric matrix A and on n given real numbers s1≦s2≦…≦sn under which a diagonal matrix V can be found so that A + V has sl,…,sn as its eigenvalues. Our motivation for this problem and our method of attack on it in [4]p comes chiefly from the work of Hadeler [5] in which sufficient conditions were given for existence of the desired diagonal V. Hadeler's approach in [5] relied heavily on the Brouwer fixed point theorem and this was also our main tool in [4]. Subsequently, using properties of topological degree, Hadeler [6] gave somewhat different conditions for the existence of the diagonal V. It is our desire here to follow this lead and to use degree theory to give some results extending those in [6] to the multiparameter case.

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