A time stepping scheme is used for the transient analysis and a homotopy method is adopted to solve the process.
时域上采用精细算法进行离散，并应用同伦算法进行求解。
We utilized the combined maximum entropy homotopy method to solve the general nonconvex nonlinear programming problems.
利用组合极大熵同伦方法，研究一般的非凸非线性规划问题。
We defined the new quasi-cone condition, established the homotopy equation and proved the global convergence of this homotopy method.
通过对可行域定义新的拟锥条件，给出相应同伦方程，并证明此同伦算法在此拟锥条件下具有全局收敛性。
Most of geophysical inversion are non-linear problems, the homotopy method based on path tracking is effective method for solving this kind of problems.
地球物理反问题大部分是非线性问题，基于路径跟踪的同伦法是求解该类问题的有效方法。
We prove that when the homotopy map is a regular map, the K-K-T point obtained from this homotopy method must be a local optimal solution by choosing proper homotopy equation.
证明了同伦映射为正则映射的条件下，选取合适的同伦方程，用此同伦方法得到的K-K-T点一定是问题局部最优解。
To improve the learning efficiency and global convergence we present the monotone homotopy method, which has the same convergence as the Newton's method, to train the weights of the network.
为改进网络学习效率及大范围收敛性，提出了网络权值学习的单调同伦方法，该方法具有与牛顿法相同的二阶收敛性。
In this paper we construct a new interior-point homotopy method for solving fixed-point problem in nonconvex set, and prove the convergence under the weak normal cone condition see Definition 2.
本文构造了一个新的求解非凸区域上不动点问题的内点同伦算法，并在弱法锥见定义2。
Under several suitable transformations, the problem of positive solutions for set-valued condensing mapping equation in an ordered locally convex topological space is studied by some homotopy method.
本文用某种同伦方法，借助于一些适当的变换，讨论了有序的局部凸拓扑线性空间中集值凝聚映象方程的正解问题。
In consideration of the drawbacks in conventional acoustic impedance inversion method, the homotopy method with vast convergence was applied to the acoustic impedance inversion in seismic exploration.
文章针对传统的声波阻抗反演方法的不足，将大范围收敛的同伦方法用于地震勘探声波阻抗的反演。
Using the homotopy analysis method, the approximation solution is obtained.
利用同伦分析方法，得到了该模型的近似解。
Using the homotopy analysis method, the approximation of the solution for the model was obtained.
利用同伦分析方法，得到了该模型解的近似展开式。
The paper reviews Some applications of the homotopy perturbation method to nonlinear differential and integral equations.
本文一篇综述类文章，综述了同伦摄动方法及它在非线性微积分方程中的某些应用。
A new asymptotic numerical method for nonlinear dynamic equations was proposed. In this method, the homotopy perturbation method was improved by using the precise integration technique.
利用精细积分技术对同伦摄动方法进行了改进，构造了一种求解非线性动力学方程的新的渐近数值方法。
The computational software is developed, which is based on the test of even change point, homotopy continuation algorithm and the iterative method.
基于上述研究，论文还研制了均值变点检验、同伦延拓法及迭代法的计算软件。
In chapter 4, Homotopy perturbation method is successfully extended to solve time-fractional diffusion equation with a moving boundary condition and an approximate solution is obtained.
在第4章，同伦摄动的方法被成功应用到求解带有一个可动边条件的时间分数阶扩散方程并且得到了一个近似解。
Case studies show that homotopy continuation method is an effective algorithm for the calculation of various nonideal systems separation with not high requirements for initial value.
实例计算表明同伦函数法是一种对初值要求不高，对各种非理想物系分离计算效果较好的一种算法。
In this paper, the method of solving nonlinear equilibrium state of aircraft is studied according to homotopy concept.
运用同伦方法的基本思想研究飞机非线性平衡状态的求解。
In this paper, the sixth-order approximate analytical solutions of the strong nonlinear oscillation with positive damping are obtained by using newly developed homotopy analysis method.
阐述利用最新提出的同伦分析方法求解有正阻尼的强非线性振动方程，得到了该方程的六阶近似解析解。
The existence and convergence of the homotopy path are proved, and efficiency of our method is illustrated by the numerical experimentations at last.
我们给出同伦路径的存在性和收敛性证明，并通过数值实验验证新算法的有效性。
Moreover, a continuous method is employed to modify the homotopy parameter during iteration in order to ensure the ability of the iteration and the capability of the noise resistance.
为保证迭代稳定性，并同时削弱观测噪声的影响，同伦参数的修正采用了连续化修正方法。
Recently, a combined homotopy interior point method (denoted as CHIP method for convenience) was presented to solve a class of nonlinear programming problems.
最近学者们提出了组合同伦内点法（简记为CHIP方法）去求解一类非线性规划问题。
The problem for getting K T point of nonlinear programming by combined homotopy interior point method under linearly independent constraint qualification is discussed at [1].
文献 [1 ]讨论了在线性无关的约束规定下 ，用组合同伦内点法求解非线性规划的KT点问题。
By using the generalized homotopy iteration method, the sets of nonlinear synthesis equations were solved, and the whole numerical solutions were given out as a result.
运用齐次化同伦连续法给出了两组非线性设计方程组的数值解。
The algorithm introduces the homotopy continuation method into the IIR adaptive filtering, which may provide a high stability for IIR filter without any stability monitoring attached.
这种算法可以在无需任何外加稳定性监控的情况下，为自适应IIR滤波器提共高的稳定性。
In this paper, we present a new interior point method-combined homotopy interior point method.
利用组合极大熵同伦方法，研究一般的非凸非线性规划问题。
The homotopy analysis method has been successfully applied to a lots of different types of nonlinear problems in science and engineering so as to prove its general validity in a wide region of fields.
应用“同伦分析方法”成功求解了科学和工程中众多类型的非线性问题，证实了其有效性和普遍适用性。
The homotopy analysis method has been successfully applied to a lots of different types of nonlinear problems in science and engineering so as to prove its general validity in a wide region of fields.
应用“同伦分析方法”成功求解了科学和工程中众多类型的非线性问题，证实了其有效性和普遍适用性。
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