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(Solved) [Polynomial interpolation and error estimation. 2+2+2+2pt] Let us interpolate the function f : [0,1] + R defined by f(3:) = exp(3x) using the nodes...


Let us interpolate the function f:[0,1] --> R defined by f(x) = exp(3x) using the nodes xi = i/2, i = 0,1,2 by a quadratic polnomial p2 e P2.

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4. [Polynomial interpolation and error estimation. 2+2+2+2pt] Let us interpolate the
function f : [0,1] —+ R defined by f(3:) = exp(3x) using the nodes 222- = *6/2, 1' = 0, 1, 2
by a quadratic polynomial pg 6 P2. (a) Use the monomial basis 1,x,332 and compute (numerically) the coefficients cj E R
such that 10201:) = 23:003-133.. Plot p2 and f in the same graph. (b) Give an alternative form for p2 using Lagrange interpolation polynomials [10(33): L1(53)
and L2(x). Plot the three Lagrange basis polynomials in the same graph. (c) COmpare the exact interpolation error Ef(3:) :2 f(3:) — 332(3):) at :c = 3/4 with the
estimate
Mn+1 IEftxn 2 (RH)! |7Tn+l(x)|)

 


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