代数流形

代数流形上的插值问题

Interpolation Problems on Algebraic Manifolds

研究高维空间中代数流形上多项式空间的Lagrange插值问题。

We researched the problem of Lagrange interpolation of polynomial space on the algebraic manifold .

代数流形上的Lagrange插值和Hermite插值

Lagrange Interpolation and Hermite Interpolation Along the Algebraic Manifold

高维空间中代数流形上多项式空间的维数与Lagrange插值适定结点组的构造

The Dimension of Polynomial Space and the Construction of Properly Posed Set of Nodes for Lagrange Interpolation on Algebraic Manifold

代数流形上多元有理插值问题的研究

The Study of the Multivariate Rational Interpolation Problems on Algebraic Mainfolds

证明了在充分相交的代数流形上任意次插值适定结点组的存在性；

The existence of properly posed set of nodes of arbitrary degree for interpolation on the algebraic manifold of sufficient intersection was proved .

建立了Lie群和Lie代数、Riemannian流形与空间算子代数理论联系的模型。

Develop the formulation of the the Lie group , Lie algebra and Riemannian manifolds and spatial operator algebra .

计算代数方程组流形解的特征值方法

The Eigenvalue Method to Compute The Manifold Solution of Algebraic Equation System

关于球面上的代数极小子流形

Algebraic Minimal Submanifolds in The Spheres

运用构造性代数几何方法，研究插值节点取在一个代数流形上时的多元多项式插值问题，提出构造极小次数插值基的相关理论和算法，并给出了极小次数插值多项式的次数估计。

Constructive algebraic geometry methods were used to discuss multivariate interpolation problems for which the interpolation nodes are taken from one algebraic manifold and the related theories and algorithms for constructing minimal degree interpolation basis were presented . An estimation for the degree of interpolation polynomial was also presented .