共查询到20条相似文献,搜索用时 15 毫秒
1.
Yongzhong Song 《BIT Numerical Mathematics》2002,42(3):611-624
In this paper, monotonicity of iterative methods for solving general solvable singularly systems is discussed. The monotonicity results given by Berman, Plemmons, and Semal are generalized to singular systems. It is shown that for an iterative method introduced by a nonnegative splitting of the coefficient matrix there exist some initial guesses such that the iterative sequence converges towards a solution of the system from below or from above. The monotonicity of the block Gauss-Seidel method for solving a p-cyclic system and Markov chain is considered. 相似文献
2.
田明 《数学的实践与认识》2009,39(23)
研究了具有重根的非线性方程的迭代方法,对基于动力系统的新牛顿类方法作了修改,改进方法仍保持了牛顿方法的二阶收敛性.数值实验结果验证了方法的有效性. 相似文献
3.
It is well known that mixed quasivariational inequalities are equivalent to implicit fixed-point problems. We use this alternative equivalent formulation to suggest and analyze a new self-adaptive resolvent method for solving mixed quasivariational inequalities in conjunction with a technique updating the solution. We show that the convergence of this method requires pseudomonotonicity, which is a weaker condition than monotonicity. Since mixed quasivariational inequalities include various classes of variational inequalities as special cases, our results continue to hold for these problems. 相似文献
4.
In this paper, we investigate the nonstationary iterative scheme for solving consistent singular linear system with index one. We utilize the group inverse to present a sufficient condition for the convergence of the nonstationary iterative method. Our result extends the known results of the stationary iterative scheme. Finally, we present a sufficient condition for the multisplitting algorithm and provide numerical examples to illustrate the advantages of nonstationary method. 相似文献
5.
本文在矩阵A为一般非奇方阵的情况下,讨论了解线性方程组AX=b的块SSOR迭代法(SSOR迭代法)的收敛性,得到了几个新的结果. 相似文献
6.
In this paper, we use the auxiliary principle technique to suggest a class of predictorcorrector methods for solving general mixed variational inequalities. The convergence of the proposed methods only requires the partially relaxed strongly monotonicity of the operator, which is weaker than co-coercivity. From special cases, we obtain various known and new results for solving various classes of variational inequalities and related problems.AMS Subject Classification (1991): 49J40, 90C33. 相似文献
7.
In this paper, two iterative schemes for approximating common element of the set of zero points of maximal monotone operators and the set of fixed points of a kind of generalized nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Two strong convergence theorems are obtained and their applications on finding the minimizer of a kind of convex functional are discussed, which extend some previous work. 相似文献
8.
Sanjay Kumar Khattri 《高等学校计算数学学报(英文版)》2012,5(4):592-601
We present a simple yet effective and applicable scheme, based on quadrature, for constructing optimal iterative methods. According to the, still unproved, Kung-Traub conjecture an optimal iterative method based on $n+1$ evaluations could achieve a maximum convergence order of $2^n$. Through quadrature, we develop optimal iterative methods of orders four and eight. The scheme can further be applied to develop iterative methods of even higher orders. Computational results demonstrate that the developed methods are efficient as compared with many well known methods. 相似文献
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10.
蒋耀林 《应用数学与计算数学学报》1995,9(1):1-5
本文在Banach空间讨论泛函f_μ(x)=∫1/p‖y_n—x‖~1dμ(n)的最小点的迭代法(这里μ是Banach极限),利用空间的特征不等式,给出了算法的弱收敛性,这里的结果在这类空间是新的。 相似文献
11.
内迭代次数充分大时,求解非奇异线性方程组的块SOR二级迭代法与经典的块SOR方法有相同的收敛性和大致相等的收敛速度.因此,用于块SOR方法有效的松弛因子,同样可有效地用于块SOR二级迭代法. 相似文献
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13.
该文给出了帐篷映射产生的迭代序列Cesaro平均收敛的条件.研究了它与实数二进展式度量性质之间的联系. 相似文献
14.
Yongzhong Song 《Annals of Operations Research》2001,103(1-4):359-369
Comparison theorems for spectral radii of two block USSOR methods, two block SSOR methods, two block AOR methods, two block SOR methods with respect to a partition and the corresponding finer partition * are given, respectively, whenever A is an M-matrix or an H-matrix. 相似文献
15.
Some Convergence Properties of Descent Methods 总被引:6,自引:0,他引:6
In this paper, we discuss the convergence properties of a class of descent algorithms for minimizing a continuously differentiable function f on R
n without assuming that the sequence { x
k
} of iterates is bounded. Under mild conditions, we prove that the limit infimum of
is zero and that false convergence does not occur when f is convex. Furthermore, we discuss the convergence rate of {
} and { f(x
k
)} when { x
k
} is unbounded and { f(x
k
)} is bounded. 相似文献
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17.
L-曲线估计确定正则参数的双网格迭代法 总被引:1,自引:0,他引:1
本文考虑对不适定问题离散化得到的大规模不适定线性方程组进行Tiknonov正则化,然后用双网格迭代法求解得到的Tikhonov正则化方程组,并用L-曲线估计法来确定正则参数.试验问题的数值结果表明双网格迭代法求解正则化后的对称正定线性方程组效果很好,且L-曲线估计法确定正则参数计算量很小. 相似文献
18.
An improvement of the iterative methods based on one point iteration function, with or without memory, using n points with the same amount of information in each point and generated by the inverse polynomial interpolation is given. The adaptation of the strategy presented here gives a new iteration function with a new evaluation of the function which increases the local order of convergence dramatically. This method is generalized to r evaluations of the function. This method for the computation of solutions of nonlinear equations is interesting when it is necessary to get high precision because it provides a lower cost when we use adaptive multi-precision arithmetics.
AMS subject classification 65H05 相似文献
19.
证明了任意实Banach空间广义Φ-增生算子的最速下降迭代序列的收敛定理,推广了ZeiqingLiu和周海云等人的近期结果. 相似文献
20.
本文讨论了用隐式Euler方法求解一类延迟量满足Lipschitz条件且Lipschitz常数小于1的非线性变延迟微分方程初值问题的收敛性.获得了带线性插值的隐式Euler方法的收敛性结果. 相似文献