In this paper, some properties of the positive definite solutions for the nonlinear system of matrix equations X + A*Y-nA = I, Y + B*X-mB = I are derived. As a matter of fact, an effective iterative method to obtain t...In this paper, some properties of the positive definite solutions for the nonlinear system of matrix equations X + A*Y-nA = I, Y + B*X-mB = I are derived. As a matter of fact, an effective iterative method to obtain the positive definite solutions of the system is established. These solutions are based on the convergence of monotone sequences of positive definite matrices. Moreover, the necessary and sufficient conditions for the existence of the positive definite solutions are obtained. Finally, some numerical results are given.展开更多
We use the method of lower and upper solutions combined with monotone iterations to differential problems with a parameter. Existence of extremal solutions to such problems is proved.
证明了{n(16n^2+4n+3)/16n^2-4~n+3^(1/2) integral from 0 to π/2 sin^nxdx}为严格单调增加数列,且极限为π/2^(1/2),因而得π(16n^2+36n+23)/2(n+1)(16n^2+28n+15)^(1/2)<integral from 0 to π/2 sin^nxdx<π(16n^2-4n+3)/2n(...证明了{n(16n^2+4n+3)/16n^2-4~n+3^(1/2) integral from 0 to π/2 sin^nxdx}为严格单调增加数列,且极限为π/2^(1/2),因而得π(16n^2+36n+23)/2(n+1)(16n^2+28n+15)^(1/2)<integral from 0 to π/2 sin^nxdx<π(16n^2-4n+3)/2n(16n^2+4n+3)^(1/2).展开更多
An algorithm for numerical solution of discrete Hamilton-Jacobi-Bellman equations is proposed. The method begins with a suitable initial guess value of the solution,then finds a suitable matrix to linearize the system...An algorithm for numerical solution of discrete Hamilton-Jacobi-Bellman equations is proposed. The method begins with a suitable initial guess value of the solution,then finds a suitable matrix to linearize the system and constructs an iteration algorithm to generate the monotone sequence. The convergence of the algorithm for nonlinear discrete Hamilton-Jacobi-Bellman equations is proved. Some numerical examples are presented to confirm the effciency of this algorithm.展开更多
文摘In this paper, some properties of the positive definite solutions for the nonlinear system of matrix equations X + A*Y-nA = I, Y + B*X-mB = I are derived. As a matter of fact, an effective iterative method to obtain the positive definite solutions of the system is established. These solutions are based on the convergence of monotone sequences of positive definite matrices. Moreover, the necessary and sufficient conditions for the existence of the positive definite solutions are obtained. Finally, some numerical results are given.
文摘We use the method of lower and upper solutions combined with monotone iterations to differential problems with a parameter. Existence of extremal solutions to such problems is proved.
文摘证明了{n(16n^2+4n+3)/16n^2-4~n+3^(1/2) integral from 0 to π/2 sin^nxdx}为严格单调增加数列,且极限为π/2^(1/2),因而得π(16n^2+36n+23)/2(n+1)(16n^2+28n+15)^(1/2)<integral from 0 to π/2 sin^nxdx<π(16n^2-4n+3)/2n(16n^2+4n+3)^(1/2).
文摘An algorithm for numerical solution of discrete Hamilton-Jacobi-Bellman equations is proposed. The method begins with a suitable initial guess value of the solution,then finds a suitable matrix to linearize the system and constructs an iteration algorithm to generate the monotone sequence. The convergence of the algorithm for nonlinear discrete Hamilton-Jacobi-Bellman equations is proved. Some numerical examples are presented to confirm the effciency of this algorithm.
