Results 211 to 220 of about 30,323 (260)
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Computing the Extremal Positive Definite Solutions of a Matrix Equation
SIAM Journal of Scientific Computing, 1996An implementation of a well-known algorithm is proposed for finding extremal positive definite solutions of the matrix equation \(X+A^*X^{-1}A=I\). The convergence rate is analyzed. Then a new algorithm is presented. This algorithm avoids matrix inversions.
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The Re-nonnegative definite and Re-positive definite solutions to the matrix equation AXB=D
Applied Mathematics and Computation, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yongxin Yuan
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Towards positive definite solutions of a class of nonlinear matrix equations
Applied Mathematics and Computation, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
James Lam, Zhao-yan Li, Bin Zhou
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Existence condition of positive-definite solutions for algebraic matrix riccati equations
Automatica, 1987Algebraic matrix Riccati equations are considered which arise in the optimal filtering as well as in control problems of continuous time-invariant systems. A necessary and sufficient condition is established for the existence of unique positive-definite solutions and the asymptotically stable closed-loop system.
Hiroyuki Kano
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On the existence of a positive definite solution of the matrix equation
International Journal of Computer Mathematics, 2001In this paper, an efficient and numerically stable algorithm for computing the positive definite solution of the nonlinear equation is proposed. Some properties of the solution are discussed as well as the sufficient conditions for the existence are obtained.
Salah M. El-Sayed, Mohamed A. Ramadan
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On positive definite solution of a nonlinear matrix equation
Numerical Linear Algebra with Applications, 2006AbstractIn this paper, some necessary and sufficient conditions for the existence of the positive definite solutions for the matrix equationX+A*X−αA=Qwith α ∈ (0, ∞) are given. Iterative methods to obtain the positive definite solutions are established and the rates of convergence of the considered methods are obtained. Copyright © 2006 John Wiley &
Zhen-Yun Peng, Salah M. El-Sayed
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Superfast Solution of Real Positive Definite Toeplitz Systems
SIAM Journal on Matrix Analysis and Applications, 1988The paper consists of three parts. The first part provides a review of the fast Fourier transformation (FFT) with emphasis on the real case. In the second part the connection between the Schur algorithm and the FFT is studied. A function \(\phi\) is called a Schur function if it maps the open unit disk D in the complex plane into its closure.
Ammar, Gregory S., Gragg, William B.
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PARALLEL SOLUTION OF SYMMETRIC POSITIVE DEFINITE TOEPLITZ SYSTEMS
Parallel Algorithms and Applications, 1997Initially, parallel algorithms were designed by parallelising the existing sequential algorithms for frequently occurring problems on available parallel architectures. More recently, parallel strategies have been identified and utilised resulting in many new parallel algorithms.
David J. Evans 0001, Gabriel Oksa
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