Here are some data points kk f(xk) 02 10 15 60 2 10 140 (a) Form the Lagrange interpolating polynomial P(x) using the original definition: P(x) = f(xk). Lk (x), = £1(² k=0 n L₁(x) = II: j=0 j/k 10 ? ? 60 ? ? 140 ? ? x-xj. Ik - Dj (b) Here is a partially completed divided differences matrix for the above data. Complete the matrix and hence form the Lagrange interpolating polynomial P(x) using the divided differences method: P(x) = f[ro]+f[x0, x₁] (x-xo)++ƒ[xo,..., n] (x-xo) (x-En-1).
Here are some data points kk f(xk) 02 10 15 60 2 10 140 (a) Form the Lagrange interpolating polynomial P(x) using the original definition: P(x) = f(xk). Lk (x), = £1(² k=0 n L₁(x) = II: j=0 j/k 10 ? ? 60 ? ? 140 ? ? x-xj. Ik - Dj (b) Here is a partially completed divided differences matrix for the above data. Complete the matrix and hence form the Lagrange interpolating polynomial P(x) using the divided differences method: P(x) = f[ro]+f[x0, x₁] (x-xo)++ƒ[xo,..., n] (x-xo) (x-En-1).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 66E
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