(0,m) Pál-type interpolation: interchanging value- and derivative-nodes

摘要

In (simple) Pál-type interpolation the problem consists of finding a polynomial of degree n+m-1 that has prescribed values at, say, n pairwise distinct points and prescribed values for the rth derivative r⩾1 at (another) set of m distinct points.The problem is named regular if it has a unique solution for any set of data; this is equivalent to the homogeneous problem (all prescribed values are 0) having the trivial solution only.In this paper the effect of interchanging the value-nodes and the derivative-nodes on the regularity of the problem is studied for several sets of nodes.