Results 221 to 230 of about 30,323 (260)
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The Hermitian Positive Definite Solution of the Nonlinear Matrix Equation
International Journal of Nonlinear Sciences and Numerical Simulation, 2017Abstract: In this paper, we study the nonlinear matrix equation X s
Zhang, Xindong, Feng, Xinlong
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Iterative Refinement of the Solution of a Positive Definite System of Equations
Numerische Mathematik, 1966In an earlier paper in this series [1] the solution of a system of equations Ax=b with a positive definite matrix of coefficients was described; this was based on the Cholesky factorization of A. If A is ill-conditioned the computed solution may not be sufficiently accurate, but (provided A is not almost singular to working accuracy) it may be improved
Martin, R. S. +2 more
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The positive definite solution to a nonlinear matrix equation
Linear and Multilinear Algebra, 2015In this paper, we consider a nonlinear matrix equation, which has the form , where is a positive integer, is an arbitrary complex matrix and is an Hermitian positive definite matrix. A double of elegant estimates of the Hermitian positive definite solution are obtained.
Jie Meng, Hyun-Min Kim
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Positive definite solution of a nonlinear matrix equation
Journal of Fixed Point Theory and Applications, 2016The authors use fixed-point theory to present a sufficient condition for the existence of a positive definite solution of the nonlinear matrix equation \(X=Q\pm\sum_{i1}^m A_i^* F(X)A_i\), where \(Q\) is a positive definite matrix, \(A_i\)'s are arbitrary \(n\times n\) matrices and \(F\) is a monotone map from the set of positive definite matrices to ...
Bose, Snehasish +2 more
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On positive definite solutions to the algebraic Riccati equation
Systems & Control Letters, 1986The authors study positive definite solutions of the algebraic Riccati equation (ARE) \(\bar AP+PA-PB\bar BP+\bar CC=0,\) where A, B, C are respectively \(n\times n\), \(n\times m\) and \(p\times n\) real matrices and \(\bar X\) denotes the transpose of X. The discussion is only on the real symmetric solution P.
Richardson, T. J., Kwong, R. H.
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On positive definite solution of nonlinear matrix equations
Linear and Multilinear Algebra, 2017AbstractIn this article, we present a sufficient condition for the existence of a unique positive definite solution of the non-linear matrix equation , where , (the set of all Hermitian positive definite matrices), are non-singular matrices and are order-preserving mappings. We give an example of a non-linear matrix equation of the above form (, A is a
Sk. Monowar Hossein +2 more
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On the positive definite solution of a class of pair of nonlinear matrix equations
Computational and Applied Mathematics, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hasem Ali, Sk Monowar Hossein
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Positive definite solutions of the nonstrict Lyapunov inequality
1997 European Control Conference (ECC), 1997Recently we have provided a full test for verifying the solvability of the nonstrict Lyapunov inequality A∗X + XA + Q ≥ 0 where A and Q = Q∗ are arbitrary. In this paper we reveal how to test the existence of a positive definite solution of the inequality.
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Non-stationary iterative solution of positive definite linear systems
International Journal of Computer Mathematics, 1999A semi-iterative method (RFII-SI method) related to the Richardson's second degree iterative method (RFII method) is developed. Both methods are applied to the class of positive definite algebraic linear systems, which includes the Ortega and the stochastic problems.
Newton R. Santos, David J. Evans 0001
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On the Positive Definite Solutions to the 2-D Continuous-time Lyapunov Equation
Multidimensional Systems and Signal Processing, 1997The very strict positive real lemma is extended for nonminimal 1-D continuous systems. New necessary and sufficient conditions for the existence of positive definite solutions to the 2-D continuous Lyapunov equation are established. Two algorithms for the solution of 2-D continuous Lyapunov equations are presented and illustrated by a numerical example.
Agathoklis, P, Xiao, C, Hill, DJ
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