Solvability problems of bivariate interpolation I

This paper is devoted to bivariate interpolation. The problem is to find a polynomialP(x, y) whose values and the values of whose derivatives at given points match given data. Methods of Birkhoff interpolation are used throughout. We define interpolation matricesE, their regularity, their almost regularity, and finally the regularity of the pairE, Z for a given set of knotsZ. Many concrete examples and applications are possible.