| AN EFFECT ITERATION ALGORITHM FOR NUMERICAL SOLUTION OF DISCRETE HAMILTON-JACOBIBELLMAN EQUATIONS |
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| 引用本文： | Cheng Xiaoliang Xu Yuanji Meng Bingquan. AN EFFECT ITERATION ALGORITHM FOR NUMERICAL SOLUTION OF DISCRETE HAMILTON-JACOBIBELLMAN EQUATIONS[J]. 高校应用数学学报(英文版), 2005, 20(3): 347-351. DOI: 10.1007/s11766-005-0011-y |
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| 作者姓名： | Cheng Xiaoliang Xu Yuanji Meng Bingquan |
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| 作者单位： | [1]Dept. of Math. , Zhejiang Univ. , Hangzhou 310028, China. [2]Dept. of Math. , Zhejiang Univ. , Hangzhou 310027, China. [3]Computer Center, Zhejiang Univ. , Hangzhou 310027, China. |
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| 基金项目： | Supported by the National Natural Science Foundation of China（10471129）. |
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| 摘 要： | §1Introduction ConsidertheHamilton-Jacobi-Bellmanequation max1≤v≤m[A(v)u(x)-f(v)(x)]=0,x∈Ω(1.1)withtheboundarycondition u(x)=0,x∈Ω(1.2)whereΩisabounded,smoothdomaininEuclideanspaceRd,d∈N;f(v)(x)aregiven functionsfromC2(Ω);A(v)aresecond-orderuniformlyellipticoperatorsoftheform A(v)=-d i,j=1a(v)ij2xixj+di=1b(v)ixi+c(v).(1.3)Intheaboveexpression(1.3)therearecoefficientsa(v)ij,b(v)i,c(v)∈C2(Ω)satisfying,forall1≤v≤m,a(v)ij(x)=a(v)ji(x),1≤i,j≤d,c(v)≥c0≥0,x∈Ω,a…
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| 关 键 词： | Hamilton-Jacobi-Bellman方程 数字算法 离散分布 线性系统 |
| 收稿时间： | 2004-10-18 |
| 修稿时间： | 2005-03-02 |
An effect iteration algorithm for numerical solution of discrete hamilton-jacobi-bellman equations |
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| Chen Xiaoliang,Xu Yuanji,Meng Bingquan. An effect iteration algorithm for numerical solution of discrete hamilton-jacobi-bellman equations[J]. Applied Mathematics A Journal of Chinese Universities, 2005, 20(3): 347-351. DOI: 10.1007/s11766-005-0011-y |
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| Authors: | Chen Xiaoliang Xu Yuanji Meng Bingquan |
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| Affiliation: | (1) Dept. of Math., Zhejiang Univ., 310028 Hangzhou, China;(2) Dept. of Math., Zhejiang Univ., 310027 Hangzhou, China;(3) Computer Center, Zhejiang Univ., 310027 Hangzhou, China |
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| Abstract: | 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. |
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| Keywords: | iteration algorthm Hamilton-Jacobi-Bellman equation monotone sequence. |
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