The Instability Degree in the Dimension of Spaces of Bivariate Splinel

In this paper, the concept of the instability degree in the dimension of spaces of bivariate spline is presented. The dimension of spaces of bivariate splines on the Morgan-Scott triangulation are considered. The dimension of the space of splines with degree 2 and with smoothness order known to be instability is extended to the space of splines of degree less than 2 and smoothness order . The dimension of the spline space on the Morgan-Scott triangulation make us conjecture the instability degree in the dimension of spaces of bivariate spline is infinity