Two Kinds of Nonlinear Matrix Equations and their Corresponding Matrix Sequences
نویسندگان
چکیده
We studied the existence and uniqueness of solutions of the following two kinds of nonlinear matrix equations X = Pk−1 l=0 P T l X lPl, and X = Pk−1 l=0 (P T l XPl) αl , and the convergence of the matrix sequences {Xi} recursively defined by Xn+k = Pk−1 l=0 P T l X αl n+lPl, n ≥ 0, and Xn+k = Pk−1 l=0 (P T l Xn+lPl) αl , n ≥ 0, where |αl| ≤ 1 for 0 ≤ l ≤ k − 1 and X0, · · · , Xk−1 are initial positive definite matrices. AMS classification: 40A05; 15A24
منابع مشابه
Analytical aspects of the interval unilateral quadratic matrix equations and their united solution sets
This paper introduces the emph{interval unilateral quadratic matrix equation}, $IUQe$ and attempts to find various analytical results on its AE-solution sets in which $A,B$ and $CCC$ are known real interval matrices, while $X$ is an unknown matrix. These results are derived from a generalization of some results of Shary. We also give sufficient conditions for non-emptiness of some quasi-solutio...
متن کاملThe Sine-Cosine Wavelet and Its Application in the Optimal Control of Nonlinear Systems with Constraint
In this paper, an optimal control of quadratic performance index with nonlinear constrained is presented. The sine-cosine wavelet operational matrix of integration and product matrix are introduced and applied to reduce nonlinear differential equations to the nonlinear algebraic equations. Then, the Newton-Raphson method is used for solving these sets of algebraic equations. To present ability ...
متن کاملWilson wavelets for solving nonlinear stochastic integral equations
A new computational method based on Wilson wavelets is proposed for solving a class of nonlinear stochastic It^{o}-Volterra integral equations. To do this a new stochastic operational matrix of It^{o} integration for Wilson wavelets is obtained. Block pulse functions (BPFs) and collocation method are used to generate a process to forming this matrix. Using these basis functions and their operat...
متن کاملDirect method for solving nonlinear two-dimensional Volterra-Fredholm integro-differential equations by block-pulse functions
In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra-Fredholm integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions.First, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. Then, by using this matrices, the nonlinear two-dimensional Vol...
متن کاملDirect method for solving nonlinear two-dimensional Volterra-Fredholm integro-differential equations by block-pulse functions
In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra-Fredholm integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions.First, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. Then, by using this matrices, the nonlinear two-dimensional Vol...
متن کامل