The mechanical background of the bivariate spline space of degree 2 and smoothness 1 on rectangular partition is presented constructively.Making use of mechan- ical analysis method,by acting couples along the interior edges with suitable evaluations, the deflection surface is divided into piecewise form,therefore,the relation between a class of bivariate splines on rectangular partition and the pure bending of thin plate is established.In addition,the interpretation of smoothing cofactor and conformality con- dition from the mechanical point of view is given.Furthermore,by introducing twisting moments,the mechanical background of any spline belong to the above space is set up.
In this paper, we obtain a properly posed set of nodes for interpolation on a sphere. Moreover it is applied to construct properly posed set of nodes for Lagrange interpolation on the trivariate polynomial space of total degree n.
This paper introduces a new notion of weighted least-square orthogonal polynomials in multivariables from the triangular form. Their existence and uniqueness is studied and some methods for their recursive computation are given. As an application, this paper constructs a new family of Padé-type approximates in multivariables from the triangular form.
