Lagrange Interpolation method
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| Posted : Dec, 04, 2010 | Author [abdelwahab]
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agrange interpolation is a very simple way to interpolate the data as a polynomial that represents this data. The first order interpolation equation is given by:
p1(x)=L0*f0+L1*f1,
where L0=(x-x1)/(x0-x1) and L1=(x-x0)/(x1-x0).
We notice that L0=1 at x0 and =0 at x1 simillarly L1=0 at x0 and 1 at x1 which means that p1(x)=f0 at x0 and zero at x1 also p1(x)=f1 at x1 and zero at x0.
by the same way we can get a second order polinomial that more accurat for the data this second order polynomial will be
P2(x)=L0*F0+L1*F1+L2*F2,
where L0=(X-X1)*(X-X2)/(X0-X1)*(X0-X2),
L1=(X-X0)*(X-X2)/(X1-X0)*(X1-X2),
and L2=(X-X0)*(X-X1)/(X2-X0)*(X2-X1).
The following script is a simple php script for the above specification
the
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