本文主要讨论了线性流形上复对称矩阵的最小二乘问题。
This paper mainly discusses the least squares problem of complex symmetric matrices on a linear manifold.
讨论了线性流形上广义次对称矩阵反问题的最小二乘解及其逼近问题。
The least squares solution of inverse problems of generalized skew symmetric matrices and It's optimal approximation problems are discussed.
给出线性流形的定义及性质，并对线性流形的全体定义了加法与数乘运算，得到了线性流形空间。
The definition and feature of linear manifold are given. The operation of adding and multiplying is defined for entire linear manifold, hence, linear manifold space is obtained.
局部线性嵌入方法是一种应用广泛的流形学习方法，本文提出算法的一种改进，并将其应用于空间数据索引。
Locally linear embedding (LLE) is a widely-used manifold learning algorithm, in this paper we improve on the algorithm and put it to use in spatial data index.
提出了一种基于相重构和主流形识别的非线性时间序列降噪方法。
A noise reduction method in nonlinear time series based on phase reconstruction and manifold learning was proposed.
本文用多层前向神经网络求解该非线性偏微分方程，从而逼近非线性系统的中心流形。
In this paper, multi-layer feedforward neural networks are used to solve the nonlinear partial differential equation, and approach the centre manifold of the nonlinear system.
流形学习旨在获得非线性分布数据的内在结构，可以用于非线性降维。
Manifold learning attempts to obtain the intrinsic structure of non-linearly distributed data, which can be used in non-linear dimensionality reduction(NLDR).
低速语音编码主要采用参数编码方式，多带混合激励线性预测编码(MELP)是参数编码的主流形式之一。
Parameter coding is the main method of low-rate speech coding and multi-band mixed excitation linear prediction (MELP) coding is one of important parameter coding.
与现有的非线性时间序列消噪算法不同，基于主流形的消噪算法更强调时间序列的整体结构。
Different from the existent noise reduction methods in nonlinear time series, the method based on principal manifold learning emphasized more on the global structure of time series.
局部线性嵌入(LLE)算法是有效的非线性降维方法，时间复杂度低并具有强的流形表达能力。
The Locaally linear Embedding (LLE) algorithm is an effective technique for nonlinear dimensionality reduction of high-dimensional data.
根据数值流形方法的特点和岩土体的本构模型，给出了适用于非线性分析的数值流形方法的计算方法。
Based on the characteristics of the numerical manifold method and constitutive models of rock and soil mass, the formula of numerical manifold method for nonlinear analysis is presented.
当应用于惯性流形多网格算法和非线性伽略金方法时，可证明类小波增量未知元方法的收敛性。
Convergence of the wavelet-like incremental unknowns method is proved when applied in the inertial manifold multigrid algorithms(IMG)or nonlinear Galerkin methods.
然而，当高维数据所逼近或近似的一个低维流形自相交时，欧氏距离意义上的邻域不能完全反映低维点的相邻关系，往往难以体现真实的局部线性结构。
However, when the underlying lower-dimensional manifold is self-intersecting at some points, it's difficult to obtain local lower-dimensional structure from the Euclidean neighborhoods.
考虑具有介质阻尼及非线性粘弹性本构关系的梁方程，证明了它的有界吸收集和有限维惯性流形的存在性，并由此得到在一定的条件下所给偏微分方程等价于一常微分方程组的初值问题。
The equations of nonlinear viscouselastic beam are considered, The existence of absorbing set and inertial manifolds for the system are obtained, and from which we get that the P D E.
考虑具有介质阻尼及非线性粘弹性本构关系的梁方程，证明了它的有界吸收集和有限维惯性流形的存在性，并由此得到在一定的条件下所给偏微分方程等价于一常微分方程组的初值问题。
The equations of nonlinear viscouselastic beam are considered, The existence of absorbing set and inertial manifolds for the system are obtained, and from which we get that the P D E.
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