An Inversion-Free Method for Finding Positive Definite Solution of a Rational Matrix Equation [PDF]
The Scientific World Journal, 2014 A new iterative scheme has been constructed for finding minimal solution of a rational matrix equation of the form X+A*X-1A=I. The new method is inversion-free per computing step.
Fazlollah Soleymani +4 more
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Positive definite solution of two kinds of nonlinear matrix equations [PDF]
Surveys in Mathematics and its Applications, 2009 Based on the elegant properties of the Thompson metric, we prove that the following two kinds of nonlinear matrix equations X=Σi=1m Ai* XδiAi and X=Σi=1m (Ai* XAi)δi ...
Fujian Duan, Zhenyun Peng, Xuefeng Duan
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On the Positive Definite Solutions of a Nonlinear Matrix Equation [PDF]
Journal of Applied Mathematics, 2013 The positive definite solutions of the nonlinear matrix equation are discussed. A necessary and sufficient condition for the existence of positive definite solutions for this equation is derived.
Panpan Liu, Shugong Zhang, Qingchun Li
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Necessary and Sufficient Conditions for the Existence of a Positive Definite Solution for the Matrix Equation [PDF]
Journal of Applied Mathematics, 2013 In this paper necessary and sufficient conditions for the matrix equation to have a positive definite solution are derived, where , is an identity matrix, are nonsingular real matrices, and is an odd positive integer.
Naglaa M. El-Shazly
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Existence and Uniqueness of the Positive Definite Solution for the Matrix Equation X=Q+A∗(X^−C)−1A [PDF]
Abstract and Applied Analysis, 2013 We consider the nonlinear matrix equation X=Q+A∗(X^−C)−1A, where Q is positive definite, C is positive semidefinite, and X^ is the block diagonal matrix defined by X^=diag(X,X,…,X).
Dongjie Gao
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Notes on the Hermitian Positive Definite Solutions of a Matrix Equation [PDF]
Journal of Applied Mathematics, 2014 The nonlinear matrix equation, X-∑i=1mAi*XδiAi=Q, with -1 ...
Jing Li, Yuhai Zhang
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Extrapolated positive definite and positive semi-definite splitting methods for solving non-Hermitian positive definite linear systems [PDF]
, 2022 summary:Recently, Na Huang and Changfeng Ma in (2016) proposed two kinds of typical practical choices of the PPS method. In this paper, we extrapolate two versions of the PPS iterative method, and we introduce the extrapolated Hermitian and skew ...
Shokrpour, Raheleh, Ebadi, Ghodrat
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Adapting the interior point method for the solution of linear programs on high performance computers [PDF]
, 1991 In this paper we describe a unified algorithmic framework for the interior point method (IPM) of solving Linear Programs (LPs) which allows us to adapt it over a range of high performance computer architectures. We set out the reasons as to why IPM makes
Levkovitz, R +5 more
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Optimal solution approximation for infinite positive-definite quadratic programming [PDF]
, 1995 We consider a general doubly-infinite, positive-definite, quadratic programming problem. We show that the sequence of unique optimal solutions to the natural finite-dimensional subproblems strongly converges to the unique optimal solution.
Benson, P. +3 more
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Convergence of block iterative methods for linear systems arising in the numerical solution of Euler equations [PDF]
, 1991 Elsner L, Mehrmann V. Convergence of block iterative methods for linear systems arising in the numerical solution of Euler equations. Numerische Mathematik.
Mehrmann, Volker, Elsner, Ludwig
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