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本文考虑纵向数据下半参数回归模型:yij=xij′β g(tij) eij,i=1,…,m,j=1,…,ni.基于最小二乘法和一般的非参数权函数方法给出了模型中参数β,回归函数g(·)和误差方差σ2的估计,并在适当条件下证明了估计量的r(r≥2)阶平均相合性. 相似文献
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本文介绍解析几何中把参数方程化为普通方程的一些常用方法。 (一)代入法通过参数方程中的一个方程求出参数的表达式,把它代入另一方程,从而消去参数,化为普通方程。例1.化下列t为参数的方程为普通方程 x=at~2+2a (1) y=at~3+2at (2) 解:由(2),得y=t(at~2+2a)(3) 把(1)代入(3),得y=tx 即 t=y/x. (4) 把(4)代入(1),得x=ay~2/x~2+2a. 整理后,得ay~2=x~3-2ax~2. (二)同解方程变形法运用同解方程组的性质,消去参数。 相似文献
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含参数的一元一次不等式在初中阶段甚至高中都是疑难问题,找到一种能解决的方法,并把它上升为思想方法,这样同类问题就能迎刃而解了.比如巧用转化思想,把含参数的方程(组)转化成不等式;合理使用分类讨论法,进行参数系数分类讨论;巧用数形结合思想方法,解决参数的取值范围. 相似文献
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双参数并行Jacobi型方法及其收敛性 总被引:11,自引:0,他引:11
1983年Missirlis提出了一种解线性代数方程组的方法,称为并行Jacobi型方法(Parallel Jacobi-Type Method)并且讨论了它的收敛性.方法的优越性在于适合并行计算.本文将这个方法推广到两个参数的情形,讨论了方法的收敛性.双参数法一方面保持了适用于并行计算的特点,而且又扩大了方法的应用范围,提高了收敛速度.事实 相似文献
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In this paper, the numerical solution of the generalized Kuramoto-Sivashinsky equation is presented by meshless method of lines (MOL). In this method the spatial derivatives are approximated by radial basis functions (RBFs) giving an edge over finite difference method (FDM) and finite element method (FEM) because no mesh is required for discretization of the problem domain. Only a set of scattered nodes is required to approximate the solution. The numerical results in comparison with exact solution using different radial basis functions (RBFs) prove the efficiency and accuracy of the method. 相似文献
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Numerical solution of fourth-order time-fractional partial differential equations with variable coefficients 下载免费PDF全文
In this paper, a numerical method for fourth-order time-fractional partial differential equations with variable coefficients is proposed. Our method consists of Laplace transform, the homotopy perturbation method and Stehfest's numerical inversion algorithm. We show the validity and efficiency of the proposed method (so called LHPM) by applying it to some examples and comparing the results obtained by this method with the ones found by Adomian decomposition method (ADM) and He's variational iteration method (HVIM). 相似文献
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For large sparse saddle point problems, we firstly introduce the block diagonally preconditioned Gauss-Seidl method (PBGS) which reduces to the GSOR method [Z.-Z. Bai, B.N. Parlett, Z.-Q. Wang, On generalized successive overrelaxation methods for augmented linear systems, Numer. Math. 102 (2005) 1-38] and PIU method [Z.-Z. Bai, Z.-Q. Wang, On parameterized inexact Uzawa methods for generalized saddle point problems, Linear Algebra Appl. 428 (2008) 2900-2932] when the preconditioners equal to different matrices, respectively. Then we generalize the PBGS method to the PPIU method and discuss the sufficient conditions such that the spectral radius of the PPIU method is much less than one. Furthermore, some rules are considered for choices of the preconditioners including the splitting method of the (1, 1) block matrix in the PIU method and numerical examples are given to show the superiority of the new method to the PIU method. 相似文献
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A new family of iterative methods for solving system of nonlinear algebric equations 总被引:1,自引:0,他引:1
Homotopy perturbation method (HPM) is applied to construct a new iterative method for solving system of nonlinear algebric equations. Comparison of the result obtained by the present method with that obtained by revised Adomian decomposition method [Hossein Jafari, Varsha Daftardar-Gejji, Appl. Math. Comput. 175 (2006) 1–7] reveals that the accuracy and fast convergence of the new method. 相似文献
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Dr. Bruce L. R. Shawyer 《manuscripta mathematica》1974,13(4):355-364
A method of summability is shown to be equivalent to the Cesàro method, (C,k) and its action on the Borel-type method, (B,α,β) gives rise to the natural scale for β. This is compared with what happens for the Abel-type method, (Aλ). 相似文献
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In this paper, the existence of solutions to a class of fractional differential equations $D_{0+}^{\alpha}u(t)=h(t)f(t, u(t), D_{0+}^{\theta}u(t))$ is obtained by an efficient and simple monotone iteration method. At first, the existence of a solution to the problem above is guaranteed by finding a bounded domain $D_M$ on functions $f$ and $g$.
Then, sufficient conditions for the existence of monotone solution to the problem are established by applying monotone iteration method. Moreover, two efficient iterative schemes are proposed, and the convergence of the iterative process is proved by using the monotonicity assumption on $f$ and $g$. In particular, a new algorithm which combines Gauss-Kronrod quadrature method with cubic spline interpolation method is adopted to achieve the monotone iteration method in Matlab environment, and the high-precision approximate solution is obtained. Finally, the main results of the paper are illustrated by some numerical simulations, and the approximate solutions graphs are provided by using the iterative method. 相似文献
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Starting from the solutions of soliton equations and corresponding eigenfunctions obtained by Darboux transformation, we present a new method to solve soliton equations with self-consistent sources (SESCS) based on method of variation of parameters. The KdV equation with self-consistent sources (KdVSCS) is used as a model to illustrate this new method. In addition, we apply this method to construct some new solutions of the derivative nonlinear Schrödinger equation with self-consistent sources (DNLSSCS) such as phase solution, dark soliton solution, bright soliton solution and breather-type solution. 相似文献
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Li-Tao Zhang Ting-Zhu Huang Shao-Hua Cheng 《Journal of Computational and Applied Mathematics》2012,236(7):1841-1850
Recently, Wu et al. [S.-L. Wu, T.-Z. Huang, X.-L. Zhao, A modified SSOR iterative method for augmented systems, J. Comput. Appl. Math. 228 (1) (2009) 424-433] introduced a modified SSOR (MSSOR) method for augmented systems. In this paper, we establish a generalized MSSOR (GMSSOR) method for solving the large sparse augmented systems of linear equations, which is the extension of the MSSOR method. Furthermore, the convergence of the GMSSOR method for augmented systems is analyzed and numerical experiments are carried out, which show that the GMSSOR method with appropriate parameters has a faster convergence rate than the MSSOR method with optimal parameters. 相似文献
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《Journal of the Egyptian Mathematical Society》2014,22(1):102-114
This paper is devoted to the numerical comparison of methods applied to solve the generalized Ito system. Four numerical methods are compared, namely, the Laplace decomposition method (LDM), the variation iteration method (VIM), the homotopy perturbation method (HPM) and the Laplace decomposition method with the Pade approximant (LD–PA) with the exact solution. 相似文献
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R. Ellahi S. Abbasbandy T. Hayat A. Zeeshan 《Numerical Methods for Partial Differential Equations》2010,26(5):1070-1078
This attempt presents the series solution of second Painlevé equation by homotopy analysis method (HAM). Comparison of HAM solution is provided with that of the Adomian decomposition method (ADM), homotopy perturbation method (HPM), analytic continuation method, and Legendre Tau method. It is revealed that there is very good agreement between the analytic continuation and HAM solutions when compared with ADM, HPM, and Legendre Tau solutions. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 相似文献