This paper analysis the local behavior of the bivariate quadratic function approximation to a bivariate function which has a given power series expansion about the origin. It is shown that the bivariate quadratic Hermite-Padé form always defines a bivariate quadratic function and that this function is analytic in a neighborhood of the origin.
The mechanical background of the bivariate spline space of degree 2 and smoothness 1 on rectangular partition is presented constructively. Making use of mechanical 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 condition 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 Pade-type approximates in multi-variables from the triangular form.
In this paper, we propose a new approach to solve the approximate implicitization problem based on RBF networks and MQ quasi-interpolation. This approach possesses the advantages of shape preserving, better smoothness, good approximation behavior and relatively less data etc. Several numerical examples are provided to demonstrate the effectiveness and flexibility of the proposed method.
