ABSTRACT
Abstract. This paper is concerned with nonnegativity preserving bivari ate C 1 interpolation to gridded data by biquadratic tensor product splines on a refined rectangular grid. The presented method requires the suitable specification of values for the first partial derivatives and the mixed second partial derivative at each data site. Sufficient nonnegativity conditions are derived utilizing the tensor product structure of the spline space and cor responding results for univariate quadratic splines with additional knots. Since the resulting system of linear inequalities for the parameters is sepa rated with respect to the data sites, the proposed fit-and-modify approach reduces to the solution of independent local quadratic programs.
