共查询到20条相似文献,搜索用时 46 毫秒
1.
本文利用区间迭代法的思想,提出一种使用单边初值条件的分裂型单调迭代方法,证明了该方法的收敛性,并且具体化到常见的单调迭代法。 相似文献
2.
本文对某些非线性方程组F(x)=0,导出了一个算法,用它可以迭代建立F(x)=0的解的紧致上、下界。算法基于某些矩阵的多分裂,因此具有自然的并行性。我们证明了趋向于解的界之收敛原则,给出了参数的收敛性区域并考察了方法的收敛速度。 相似文献
3.
有各种迭代方法.松弛型迭代法、正则化迭代法、Ishikawa迭代法、预解式迭代法以及遍历型迭代法,最引人注目.这些迭代法的计算复杂性不尽相同,对不同单调程度的映象可分别使用.例如,松弛型迭代法 相似文献
4.
本文对某些非线性方程组F(x)=0,导出了一个算法,用它可以迭代建立F(x)=0的解的紧致上、上界。算法基于某些矩阵的多分裂,因此具有自然的并行性。我们证明了趋于解的界之收敛原则,给出了参数的收敛性区域并考察了方法的收敛速度。 相似文献
5.
矩阵分裂的单调收敛性 总被引:1,自引:0,他引:1
本文在非负矩阵分裂条件下证明了迭代算法(3)的单调收敛性,它不仅推广了[1]~[5]中的相应结果,而且在比[7]中定理较弱的条件下,得到了广义AOR迭代法的单调收敛性。本文最后还给出了一个数值例子。 相似文献
6.
As a continuation of part I of the paper under the same title, we developgeneral monotonic enclosure methods for the couple systems of the splitting equations {x=G([x]a,[x]b,[y]c) y=G([y]a,[y]b,[x]c),which models the system of equations associated with hybrid and aaynchronotts monotonicity as well as convexity. The resulting algorithms and convergence theorems generalize and unify various known methods and monotonic enclosure theorents established by other authors. 相似文献
7.
高阶微分积分方程的单调迭代法及其应用 总被引:1,自引:0,他引:1
首先利用上下解方法以及微分不等式理论给出了n阶微分积分方程的初值问题解的存在性及其单调迭代法,然后将所得结果应用到n阶微分方程的两点边值问题,得到了n阶非线性两点边值问题解的存在性及其单调迭代法,所得结果推广了已有的结果. 相似文献
8.
本文对离散HJB方程提出一类新的迭代法,产生的迭代解单调收敛于HJB方程的解.此法的优点是简单易行. 相似文献
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10.
用单调迭代法研究一类三阶微分方程边值问题解的存在性,不仅证明了该问题解的存在性,而且得到了其迭代格式. 相似文献
11.
引用两种加速计算PageRank的算法,分别为内外迭代法和两步分裂迭代算法.从这两种方法中,得到多步幂法修正的内外迭代方法.首先,详细介绍了算法实施过程.然后,对此算法的收敛性进行证明,并且将此算法的谱半径与两步分裂迭代算法的谱半径进行比较.最后,数值试验说明该算法的计算速度比两步分裂迭代法要快. 相似文献
12.
白中治 《高等学校计算数学学报(英文版)》1996,(2)
Under suitable conditions,the monotone convergence about the projected iteration method for solving linear complementarity problem is proved and the influence of the involved parameter matrix on the convergence rate of this method is investigated. 相似文献
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14.
CHEN ZHENTAO 《高校应用数学学报(英文版)》1994,9(3):231-236
ONTHEEXISTENCEANDUNIQUENESSOFPOSITIVESOLUTIONSFORACLASSOFDEGENERATEELLIPTICSYSTEMS¥CHENZHENTAO(DepartmentofMathematics,Xiangt... 相似文献
15.
叶瑞松 《应用数学与计算数学学报》1996,10(1):12-17
本文构造分裂迭代算法用于计算二重对称破缺转向点,该方法将明显(?)少计算的工作量和占用的内存,并且以可调节的速度线性收敛。数值计算成功地说明了分裂迭代算法的有效性。 相似文献
16.
董云达 《高等学校计算数学学报》2010,32(3)
<正>This paper generalizes a class of projection type methods for monotone variational inequalities to general monotone inclusion.It is shown that when the normal cone operator in projection is replaced by any maximal monotone operator,the resulting method inherits all attractive convergence properties of projection type methods,and allows an adjusting step size rule.Weaker convergence assumption entails an extra projection at each iteration.Moreover,this paper also addresses applications of the resulting method to convex programs and monotone variational inequalities. 相似文献
17.
Cheng Xiaoliang Xu Yuanji Meng Bingquan 《高校应用数学学报(英文版)》2005,20(3):347-351
§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… 相似文献
18.
By further generalizing the skew-symmetric triangular splitting iteration method studied by Krukier, Chikina and Belokon (Applied Numerical Mathematics, 41 (2002), pp. 89–105), in this paper, we present a new iteration scheme, called the modified skew-Hermitian triangular splitting iteration method, for solving the strongly non-Hermitian systems of linear equations with positive definite coefficient matrices. We discuss the convergence property and the optimal parameters of this new method in depth. Moreover, when it is applied to precondition the Krylov subspace methods like GMRES, the preconditioning property of the modified skew-Hermitian triangular splitting iteration is analyzed in detail. Numerical results show that, as both solver and preconditioner, the modified skew-Hermitian triangular splitting iteration method is very effective for solving large sparse positive definite systems of linear equations of strong skew-Hermitian parts. 相似文献
19.
For the non-Hermitian and positive semidefinite systems of linear equations, we derive necessary and sufficient conditions for guaranteeing the unconditional convergence of the preconditioned Hermitian and skew-Hermitian splitting iteration methods. We then apply these results to block tridiagonal linear systems in order to obtain convergence conditions for the corresponding block variants of the preconditioned Hermitian and skew-Hermitian splitting iteration methods.
20.
周如海 《高等学校计算数学学报(英文版)》1993,(2)
In order to solve linear interval equations Ax=b. the interval Gauss-Seidel iteration is applied to a modified equations A'x = b', where A' is obtained by eliminating all elements in the first upper codiagonal part of A. It is shown that this modified Gauss-Seidel iteration converges when the usual Gauss-Seidel iteration converges, and the modified Gauss-Seidel iteration always has a smaller convergence factor. The converse is not true. It is also pointed out that the modified Gauss-Seidel iteration can obtain a belter result comparing with the usual Gauss-Seidel iteration in some cases. Several examples confirmed these conclusions. 相似文献