
<A NAME=INTERPOL>

<TITLE>INTERPOL</TITLE></A>
<b><a href=r37_idx.html>INDEX</a></b><p><p>



<B>INTERPOL</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>operator</B><P>
<P>
 
 <P>
<P>
<em>interpol</em>generates an interpolation polynomial. 
 <P> <H3> 
syntax: </H3>
<P>
<P>
interpol(&lt;values&gt;,&lt;variable&gt;,&lt;points&gt;) 
<P>
<P>
<P>
&lt;values&gt; and &lt;points&gt; are 
<A HREF=r37_0053.html>list</A>s of equal length and 
&lt;variable&gt; is an algebraic expression (preferably a 
<A HREF=r37_0002.html>kernel</A>). 
The interpolation polynomial is generated in the given variable of degree 
length(&lt;values&gt;)-1. The unique polynomial <em>f</em> is defined by the 
property that for corresponding elements <em>v</em> of &lt;values&gt; and 
<em>p</em> of &lt;points&gt; the relation <em>f(p)=v</em> holds. 
<P>
<P>
 <P> <H3> 
examples: </H3>
<P><PRE><TT>
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

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