Study On Lagrange Interpolation Of Quadric Surfaces

In the category of computational mathematics covered.Interpolation is a basic and classic problem.It is widely used in solving practical problems and scientific research.For example,in the aircraft,radar,sculpture design,each data point usually has the function relation.However,since the function relationship is difficult to express or too complicated,interpolation can generally be used to solve the above problems.That is,from the geometric point of view,it is through the given set of data points to construct the difference function to describe the approximate image of the surface.The Lagrange interpolation problem on the quadratic surface is discussed and studied.It is divided into three parts for introduction.The first part mainly summarizes the previous research results.It is divided into three sections.The first section introduces the origin on the problem of multivariate polynomial interpolation.The second section introduces the related problems of binary polynomial interpolation and interpolation regular node group.In the third section,we introduce the multivariate polynomial interpolation.The second part firstly introduces some multiple Lagrange interpolation from two directions.One is the Lagrange interpolation of the plane algebraic curve and the other is Lagrange interpolation of the space algebraic surface.Which gives the predecessors research by the"add the straight-line method"to construct regular plane algebraic curve interpolation node groups,"added plane method"to construct the algebraic surface interpolation regular node groups,"added algebra curve method"to construct_nP^?7?2?8?,_nP^?7?3?8?,interpolation of the regular node group.The third part is the core content of my master thesis.This part mainly studies the Lagrange interpolation problem on the quadric surface,which mainly analyzes the ellipsoid surface and the rotating paraboloid.On the basis of the previous research results,the"adding ellipsoidal surface method"and"adding rotating paraboloidal method"were put forward to construct_nP^?7?3?8?interpolation regular node group,and the corresponding theorem proving.In the end,we use the"add ellipsoid method"and"add rotating paraboloid method"to carry out the experiment calculation example,compare and analyze,and use Matlab software to further realization.