INTERPOL _ _ _ _ _ _ _ _ _ _ _ _ operator

interpolgenerates an interpolation polynomial.

syntax:

interpol(<values>,<variable>,<points>)

<values> and <points> are lists of equal length and <variable> is an algebraic expression (preferably a kernel). The interpolation polynomial is generated in the given variable of degree length(<values>)-1. The unique polynomial f is defined by the property that for corresponding elements v of <values> and p of <points> the relation f(p)=v holds.

examples:

f := for i:=1:4 collect(i**3-1); 

  F := 0,7,26,63 


p := {1,2,3,4}; 

  P := 1,2,3,4 


interpol(f,x,p); 

   3
  X  - 1

The Aitken-Neville interpolation algorithm is used which guarantee s a stable result even with rounded numbers and an ill-conditioned problem.