The Explicit Representation Of The Inverse Vandermonde Matrix With Multiple Knots And Its Application To Full Hermite Interpolation

The term Hermite interpolation refers to the interpolation of a function and some of its derivatives at a set of nodes. We always make use of Lagrange interpolation basis function and multiple difference quotient to solve the problem. The former is favorable to the thought, but the solution is too troublesome;the latter is inconvenient to the thought.There have been many results about Hermite interpolation. This paper is devoted to discuss the explicit representation of the inverse Vandermonde matrix with multiple knots and its application to Pull Hermite interpolation. First, we introduce the definition of Full Hermite interpolation and the Vandermonde matrix, and two lemmas which are most important for solving the problem. Secondly, we consider of the representation of the inverse Vandermonde matrix with multiple knots. Two examples about inverse Vandermonde matrix with multiple knots are given. At last, we introduce the application to Full Hermite interpolation.