Results 231 to 240 of about 30,323 (260)

Positive Definite Solutions of the Equation X + A*X -n A=I

2001
The general nonlinear matrix equation X + A* X-n A = I is discussed (n is a positive integer). Some necessary and sufficient conditions for existence a solution are given. Two methods for iterative computing a positive definite solution are investigated. Numerical experiments to illustrate the performance of the methods are reported.
Vejdi Hassanov, Ivan Ivanov
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Distributed solution of sparse symmetric positive definite systems

Proceedings of Scalable Parallel Libraries Conference, 2002
We consider the solution of a linear system Ax=b on a distributed memory machine when the matrix A is large, sparse and symmetric positive definite. In a previous paper we developed an algorithm to compute a fill-reducing nested dissection ordering of A on a distributed memory machine.
M.T. Heath, P. Raghavan
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Positive definiteness in the numerical solution of Riccati differential equations

Numerische Mathematik, 1994
We address the issue of integrating symmetric Riccati and Lyapunov matrix differential equations. In many cases -- typical in applications -- the solutions are positive definite matrices. Our goal is to study when and how this property is maintained for a numerical computed solution.
Dieci, Luca, Eirola, Timo
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Positive-definite self-dual solutions of Einstein’s field equations

Journal of Mathematical Physics, 1983
We investigate (anti-) self-dual Riemann space-times for diagonal Bianchi types of class A with positive-definite metrics. A general algorithm to find self-dual solutions is presented. Explicit solutions are given for all types of class A.
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The Hermitian Positive Definite Solution of Some Matrix Equations

2009 Asia-Pacific Conference on Information Processing, 2009
In this paper, the Hermitian positive definite solutions of the nonlinear matrix equation are studied. We discuss the relation between and by the eigen value and eigenvector of and respectively, and the property of numerical range of . An iterative method for obtaining positive definite solutions of the equation is constructed.
Xuetting Liu, Peiyu Wei
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On Hermitian positive definite solutions of nonlinear matrix equation

2011 International Conference on System science, Engineering design and Manufacturing informatization, 2011
In this paper, the Hermitian positive definite solutions of the nonlinear matrix equations X + A*X−qA = Q and X − A*X−qA = Q are discussed where q∈(0,1]. Some sufficient conditions for the existence of Hermitian positive definite solutions for these equations are derived.
null Qingchun Li, null Panpan Liu
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On the Existence of Extremal Positive Definite Solutions of a Kind of Matrix Equation

International Journal of Nonlinear Sciences and Numerical Simulation, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Hermitian Positive Definite Solution of Nonlinear Matrix Equations

2009 International Conference on Computer Technology and Development, 2009
In this paper, we study the Hermitian positive definite solutions of the nonlinear matrix equation $X+A* X^{-2} A+I$. Suppose $X$ is a Hermitian positive definite solution of this equation. We discuss the relation between $X$ and $A$ by the eigenvalue and eigenvector of $X$ and $A$ respectively.
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A Solution of the Completion Problem of Symmetric Positive Definite Matrices

Proceedings, 2012
A solution of the completion problem of symmetric positive definite matrices. Symmetric positive definite matrices play an important role in statistics. Typical examples are the covariance and correlation matrices which capture the second order statistics between random variables.
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Positive Definite Solution of a Class of Matrix Equations

Innovation, 2023
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