iterative method for mirror-symmetric solution of matrix equation axb + cy d = e
Abstract
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This paper is concerned with numerical solutions to general linear matrix equations including the wellknown Lyapunov matrix equation and Sylvester matrix equation as special cases. Gradient based iterative algorithm is proposed to approximate the exact solution. A necessary and s
By simply transforming the quadratic matrix equation into an equivalent fixed-point equation, we construct a successive approximation method and a Newton’s method based on this fixed-point equation. Under suitable conditions, we prove the local convergence of these two methods, a
In this paper, we consider Newton’s method and Bernoulli’s method for a quadratic matrix equation arising from an overdamped vibrating system. By introducing M-matrix to this equation, we provide a sufficient condition for the existence of the primary solution. Moreover, we show
We prove a convergence result for an iterative method, proposed recently by B. Meini, for finding the maximal Hermitian positive definite solution of the matrix equationX+A∗X−1A = Q, where Q is Hermitian positive definite.