- #1

e.gedge

- 7

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l

_{j}(t)= (t-a

_{0}) ...(t-a

_{j-1})(t-a

_{j+1})...(t-a

_{n}) / (a

_{j}-a

_{0})...(a

_{j}-a

_{j-1})(a

_{j}-a

_{j+1})...(a

_{j}-a

_{n})

A) compute the lagrange polynomials associated with a

_{0}=1, a

_{1}=2, a

_{2}=3. Evaluate l

_{j}(a

_{i}).

B) prove that (l

_{0}, l

_{1}, ... l

_{n}) form a basis for R[t] less than or equal to n.

C) Deduce the Lagrange interpolation formula.

Thanks!