Can any one explain this formula "Lagrange Interpolating Polynomial" to me in plain English.

Is there any program around to calc this formaula?

Thanks.

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- Feb 16th 2006, 01:43 AMBanderHMLagrange Interpolating Polynomial!
Can any one explain this formula "Lagrange Interpolating Polynomial" to me in plain English.

Is there any program around to calc this formaula?

Thanks. - Feb 16th 2006, 04:20 AMCaptainBlackQuote:

Originally Posted by**BanderHM**

is a polynomial of degree $\displaystyle n$ (the number of data points) which passes exactly

through each of the data points. It can be written explicitly in terms of the

data as shown below:

Consider the polynomials:

$\displaystyle

P_i(x)=\prod_{j=1,\ j \ne i}^n \frac{x-x_j}{x_i-x_j}

$,

This equals $\displaystyle 1$ at $\displaystyle x=x_i$, and equals $\displaystyle 0$ when $\displaystyle x=x_j\ ,j \ne i$.

Hence:

$\displaystyle

P(x)=\sum_{i=1}^n\ y_i\ P_i(x)

$

is a polynomial such that $\displaystyle P(x_i)=y_i, \ \mbox{i=1,\ ..\ n}$.

This is the Lagrange interpolating polynomial for the data $\displaystyle (x_i,y_i),\ i=1,\ ..\ n$.

There is one more thing to say about Lagrangian interpolation, and that is

it is of more importance to theory than practice. If you actualy want to

interpolate on real data there are almost always better ways of doing so

than Lagrangian interpolation.

RonL - Feb 16th 2006, 01:54 PMBanderHMHow?Quote:

Originally Posted by**CaptainBlack**

Thanks. - Feb 16th 2006, 02:17 PMCaptainBlackQuote:

Originally Posted by**BanderHM**

the list is almost endless

RonL