共查询到20条相似文献,搜索用时 703 毫秒
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王连堂 《高等学校计算数学学报》1997,19(4):364-369
1 引言 1968年地质学家G Backus and F Gilbert给出了求解线性(非线性)矩问题的一种方法,用来求解地球物理反问题。后来称这种方法为B-G方法。过去几年,数学家们从理论和应用方面研究了B-G方法。从理论上分析了其收敛性并给出了误差估计。第一类算子方程在不同函数空间的离散化得到不同形式的矩问题。[4]、[5]研究了再生核空间和小波空间的B-G方法。并用于信号恢复问题。由于矩问题的不适定性,有必要分析B-G方法解的正则性,本文得到了B-G方法对不精确数据的误差估计,从而证明了B-G方法是—种正则化方法。 考虑线性矩问题 相似文献
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给出一种求解线性矩问题的逼近方法,并给出以B样条函数为基的数值例子,证明了该方法的有效性. 相似文献
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迭代根问题是嵌入流的一个弱问题.关于单调函数的迭代根已有较多结论.但是对非单调函数迭代根的研究却很困难的.分式线性函数是一类实数域上的非单调函数.本文对复平面上分式线性函数的迭代根进行了研究.将分式线性函数的迭代函数方程与一个商空间上的矩阵方程对应,并运用一个求解矩阵根的方法,得到其所有亚纯迭代根的一般公式.并且确定了不同情形下分式线性函数迭代根的准确数目. 作为应用,分别给出了函数$z$和函数$1/z$全部亚纯迭代根. 相似文献
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王建宏 《数学的实践与认识》2011,41(12)
系统和控制理论中许多重要的问题,都可转化为具有线性目标函数、线性矩阵不等式约束的LMI优化问题,从而使其在数值上易于求解.本文给出一种求解LMI优化问题的原对偶中心路径算法,该算法利用牛顿方法求解中心路径方程得到牛顿系统,并将该牛顿系统对称化以避免得到非对称化的搜索方向.文章详细分析了算法的计算复杂性. 相似文献
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将Matthies,Skrzypacz和Tubiska的思想从线性的Oseen方程拓展到了非线性的Navier-Stokes方程,针对不可压缩的定常Navier-Stokes方程,提出了一种局部投影稳定化有限元方法.该方法既克服了对流占优,又绕开了inf-sup条件的限制.给出的局部投影空间既可以定义在两种不同网格上,又可以定义在相同网格上.与其他两级方法相比,定义在同一网格空间上的局部投影稳定化格式更紧凑.在同一网格上,除了给出需要bubble函数来增强的逼近空间外,还特别考虑了两种不需要用bubble函数来增强的新的空间.基于一种特殊的插值技巧,给出了稳定性分析和误差估计.最后,还列举了两个数值算例,进一步验证了理论结果的正确性. 相似文献
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高阶波动方程的时空估计与低能量散射 总被引:2,自引:1,他引:1
本文研究了高阶波动方程的低能量散射理论,基本工具是高阶线性波动方程解的时空估计.与经典的二阶波动方程解的时空估计证明不同,我们采用泛函分析的方法与待定指标技巧,首次给出了高阶线性波动方程的时空估计,藉此与非线性函数在齐次Sobolev空间中的估计,获得了高阶波动方程的低能量散射结论.与此同时,也得到了具临界增长的高阶波动方程的柯西问题在低能量条件下的整体存在唯一性. 相似文献
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一类非线性波动方程的势对称分类 总被引:1,自引:0,他引:1
先给出了含有一个任意函数的线性波动方程的古典和势对称的完全分类.然后,在此基础上给出了含有两个任意函数的一类非线性波动方程的两种情形势对称分类,得到了该方程的新势对称.在处理对称群分类问题的难点-求解确定方程组时我们提出了微分形式吴方法算法,克服了以往难于处理的困难.在整个计算过程中反复使用了吴方法,吴方法起到了关键的作用. 相似文献
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提出一些改进的方法来计算矩阵A的平方根,也就是应用一些牛顿法的变形来解决二次矩阵方程.研究表明,改进的方法比牛顿算法和一些已有的牛顿算法的变形效果要好.通过迭代方法,举出一些数值例子说明改进的方法的性能. 相似文献
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Asghar Ghorbani Jafar Saberi-Nadjafi 《Nonlinear Analysis: Real World Applications》2009,10(5):2828-2833
It is well known that one of the advantages of He’s variational iteration method is the free choice of initial approximation. Therefore, in this paper, we use this advantage to propose a reliable modification of He’s variational iteration method. Indeed, this constructs an initial trial-function without unknown parameters, which is called the modified variational iteration method. Some of the nonlinear and linear equations are examined by the modified method to illustrate the effectiveness and convenience of this method, and in all cases, the modified technique performed excellently. The results reveal that the proposed method is very effective and simple and gives exact solutions. The modification could lead to a promising approach for many applications in applied sciences. 相似文献
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Yueting Yan Chengxian Xu 《高等学校计算数学学报(英文版)》2006,15(3):257-267
In this paper, a switching method for unconstrained minimization is proposed. The method is based on the modified BFGS method and the modified SR1 method. The eigenvalues and condition numbers of both the modified updates are evaluated and used in the switching rule. When the condition number of the modified SR1 update is superior to the modified BFGS update, the step in the proposed quasi-Newton method is the modified SR1 step. Otherwise the step is the modified BFGS step. The efficiency of the proposed method is tested by numerical experiments on small, medium and large scale optimization. The numerical results are reported and analyzed to show the superiority of the proposed method. 相似文献
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A zero-finding technique in which the order of convergence is improved and nonlinear equations are solved more efficiently than they are solved by traditional iterative methods is derived. Composing a modified Chebyshev-Halley method with a variant of this method that just introduces one evaluation of the function the iterative methods presented are obtained. By carrying out this procedure the output numerical results show that the new methods compete in both order and efficiency with the modified Chebyshev-Halley methods. 相似文献
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Variational iteration method is introduced to solve the modified equal width equation. This method provides remarkable accuracy in comparison with the analytical solution. Three conservation quantities are reported. Numerical results demonstrate that this method is a promising and powerful tool for solving the modified equal width equation. 相似文献
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Xiang-Tuan Xiong 《Journal of Computational and Applied Mathematics》2010,233(8):1723-1732
We investigate a Cauchy problem for the Helmholtz equation. A modified boundary method is used for solving this ill-posed problem. Some Hölder-type error estimates are obtained. The numerical experiment shows that the modified boundary method works well. 相似文献
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Wanyou Cheng 《Numerical Functional Analysis & Optimization》2013,34(12):1372-1385
In this article, we first propose a feasible steepest descent direction for box-constrained optimization. By the use of the direction and recently developed modified PRP method, we propose a subspace modified PRP method for box-constrained optimization. Under appropriate conditions, we show that the method is globally convergent. Numerical experiments are presented using box-constrained problems in the CUTEr test problem libraries. 相似文献
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主要研究了一类状态转换下美式跳扩散期权定价模型的修正Crank-Nicolson拟合有限体积法并且给出收敛性分析.文章所构造的新方法是对[Gan X T,Yin J F,Li R,Fitted finite volume method for pricing American options under regime-switching.jump-diffusion models based on penalty method.Adv.Appl.Math.Mech.,2020,12(3):748-773]中时间方向上Crank-Nicolson格式的改进.同时,还对求解非线性系统迭代方法的收敛性证明进行了补充.最后,数值实验验证了新方法的有效性. 相似文献
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In this paper, we are concerned with the conjugate gradient methods for solving unconstrained optimization problems. It is well-known that the direction generated by a conjugate gradient method may not be a descent direction of the objective function. In this paper, we take a little modification to the Fletcher–Reeves (FR) method such that the direction generated by the modified method provides a descent direction for the objective function. This property depends neither on the line search used, nor on the convexity of the objective function. Moreover, the modified method reduces to the standard FR method if line search is exact. Under mild conditions, we prove that the modified method with Armijo-type line search is globally convergent even if the objective function is nonconvex. We also present some numerical results to show the efficiency of the proposed method.Supported by the 973 project (2004CB719402) and the NSF foundation (10471036) of China. 相似文献