Show that Lagranges interpolation formula for cubic interpolation is Use this formula to find a cubic polynomial

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Show that Lagrange’s interpolation formula for cubic interpolation is

f(x) = (x-x)(x-x)(x (xox)(xox)(x x3) - x) - + (x-x)(x-x)(x - x) + -fi (x - x0)(x - x)(x - x3) -fo

Use this formula to find a cubic polynomial that fits the function f given in the following table:

x fox) -1 - 1 0 0 1 1 2 8

Draw the graph of the cubic for –1 1/3.

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Modern Engineering Mathematics

ISBN: 9781292253497

6th Edition

Authors: Glyn James

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Question Posted: Jan 04, 2024 06:16 AM

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Show that Lagranges interpolation formula for cubic interpolation is Use this formula to find a cubic polynomial

Question:

f(x) = (x-x)(x-x)(x (xox)(xox)(x x3) - x) - + (x-x)(x-x)(x - x) + -fi (x - x0)(x - x)(x - x3) -fo (x-x)(x-x)(x - x) (x-x)(x-x)(x -$ x3) - (x - x)(x-x)(x - x) -f3 + - (x3 - x)(x3x)(xz - x)`

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For cubic interpolation we need four points x i f i ...View the full answer

Modern Engineering Mathematics

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