proof of uniqueness of Lagrange Interpolation formula
Existence is clear from the construction, the uniqueness is proved by assuming there are two different polynomials p(x) and q(x) that interpolate the points. Then r(x)=p(x)-q(x) has n zeros, x1,…,xn and there is a point xe such that r(xe)≠0. r(x) is non-constant with degree deg(r(x))≤n-1 and has more than n-1 solutions, which is a contradiction
. Thus there can only be one polynomial.
Title | proof of uniqueness of Lagrange Interpolation formula |
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Canonical name | ProofOfUniquenessOfLagrangeInterpolationFormula |
Date of creation | 2013-03-22 14:09:25 |
Last modified on | 2013-03-22 14:09:25 |
Owner | rspuzio (6075) |
Last modified by | rspuzio (6075) |
Numerical id | 10 |
Author | rspuzio (6075) |
Entry type | Proof |
Classification | msc 65D05 |
Classification | msc 41A05 |