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Home » Olympiad Section » Algebra » Algebra Theorems and Formulas

Lagrange interpolation formula
Moderators: High School Olympiad Moderators, Arne, darij grinberg, harazi, mathmanman, Megus, N.T.TUAN, orl, pbornsztein

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sj0201
Poincare Conjecture

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Lagrange interpolation formula
example?

Can someone possibly give an example of when and how one would use the Lagrange interpolation formula?

Posted: Thu Aug 06, 2009 10:02 pm

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Allnames
Yang-Mills Theory

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Re: Lagrange interpolation formula
example?

sj0201 wrote:

Can someone possibly give an example of when and how one would use the Lagrange interpolation formula?

When?: When the exercise ( or problem) gives us values of $P(x)$ at more $deg P$ points. Let think of the Lagrange interpolation formula?
For example: Let $P(x)$ be a $n$ -degree polynomial , and $P(i)=\frac{i}{i+1} \forall 0\le i\le n$ . Find $f(n+1)$ (USAMO 1975 and GB MO 1989)
Or it helps us in finding and proving some special indentities, or inequalities , or bounds for polynomials.

Posted: Fri Aug 07, 2009 8:03 am

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