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<HTML>
<HEAD>
<TITLE>Lagrange interpolation</TITLE>
</HEAD>
<BODY bgcolor="#FFFFFF" fgcolor="#000000">
<P><A NAME="interpolate"></A>
<font size="+3" color="green"><B>Lagrange interpolation</B></font></P>
<P>
<TABLE border="1" cols="2" frame="box" rules="all" width="572">
<TR>
<TD width="15%" valign="top"><B>Syntax</B>:</TD>
<TD width="85%"><CODE>
vout = INTERPOLATE(x,y,xout,'LAGRANGE')</CODE>
</TD></TR>
</table></p>
<p>
If the <CODE>LAGRANGE</CODE> keyword is used, the
interpolating method used is general Lagrange interpolation. The degree of
the interpolating polynomial depends on the number of input data points.</P>
<P>
Suppose that <CODE>N</CODE> is the number of points, equal to the lengths of
<CODE>x</CODE> and <CODE>y</CODE>. If <CODE>N = 2</CODE>,
then a simple straight line is used for interpolating. If <CODE>N = 3</CODE>
or <CODE>N = 4</CODE>, then a quadratic is used. If <CODE>N ≥ 5</CODE>,
then a polynomial of degree <CODE>4</CODE> is used for the interpolation.</P>
<P>
<a href="linear.htm"><img align=middle border="0" src="../../../shadow_left.gif">
<font size="+1" color="olive">Linear interpolation</font></a><br />
<a href="fc.htm"><img align=middle border="0" src="../../../shadow_right.gif">
<font size="+1" color="olive">Fritch-Carlson interpolation</font></a>
</P>
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