Yi Using a \"CUBIC -3-rd order \"interpolation function be computed as (LAGRANGE
ID: 1713362 • Letter: Y
Question
Yi Using a "CUBIC -3-rd order "interpolation function be computed as (LAGRANGE method), the value of Y (at X -7) carn ()0.4123 (b) 1.3214 (c) 1.3214(d) -0.3214 (e) none of the above Problem 07 Given the following data xi = - 1.00 2.00 6.00 8.00 1.00 3.00 -2.00 5.00 Using a “ CUBIC = 3-rd order "interpolation function (DIVIDED DIFFERENCE method), the CUBIC interpolation function can be expressed as F3(x) bo+ b1 (X-1) +b2 (X-1)*(X-2) +b3 * (X-1) * (X-2) * (X-6) And the unknown constants (bo, b1, b2, b3) can be computed as (o) (1, 2, 0.65, 0.20595) (b) (1,-0.65, 2, 0.20595) (d) (1, 2, 0.59502, 0.65) (d) (1, 2,-0.65, 0.20595) (e) none of the aboveExplanation / Answer
We have,interpolation function as
F(X)=b0+b1*(x-1)+b2*(x-1) * (x-2) + b3 * (x-1) * (x-2) * (x-6)
putting value of xi in function
F(1)=b0 = 1
F(2) = b0 + b1 * (2-1)
3= 1 + b1 * (2-1)
b1 = 2
F(6) = 1 + 2 * (6-1) + b2 * (6-1) * (6-2) = -2
b2 = -0.65
F(8) = 1 + 2 * (8-1) + (-0.65) * (8-1) * (8-2) + b3 * (8-1) * (8-2) * (8-6) = 5
b3 = 0.20595
Hence, the correct answer is (d)
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