基于同伦映射的同伦算法，具有大范围收敛性。
The homotopy algorithm, basing on homotopy mapping, is convergent with wide range.
本文利用连续同伦方法讨论非线性映射在有界区域内零点的存在性和零点数目，以及推广若干经典定理。
With homotopy methods, this paper discusses the existence and the number of zeroes of nonlinear mappings on bounded regions and extends some classical theorems.
同胚映射和同伦等价是代数拓扑学中的两个重要概念。
Homeomorphic morphism and homotopy equivalence are two important concepts in the theory of algebraic topology.
结果推广了同胚映射、同伦等价和同伦正则态射的有关结果。
Results Generalizing some results of homeomorphic morphism, homotopy equivalence and homotopy regular morphism.
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。
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.
基于同伦映射的思想，改进了求解非线性反问题的梯度正则化算法。
Based on idea of homotopy mapping, an improved gradient regularization algorithm was developed.
用同伦方法分析了可分解映射的零点存在性，并获得它对一类非线性特征值问题的应用。
Using homotopy methods, this paper gives an analysis on the existence of zeros of the decomposable mapping, and finds its application to a class of nonlinear eigenvalue problems.
用同伦方法分析了可分解映射的零点存在性，并获得它对一类非线性特征值问题的应用。
Using homotopy methods, this paper gives an analysis on the existence of zeros of the decomposable mapping, and finds its application to a class of nonlinear eigenvalue problems.
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