Interpolation - Lagrange's Interpolation
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Calculus engineering math, Lagranges Interpolation, Quadratic Interpolation, Interpolating polynomial. See attached file for full problem description.
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For the description of the problem on Interpolation, please see the attached pdf file.
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Solution :
Given f(x) = x3 + x - 1 ; and 0 ≤ x ≤ 2
x F(x) F(x0 , x1 ) F(x0 , x1 , x2 ) F(x0 , x1 , x2 , x3 )
0 - 1
½ - 0.375 1.25
1 1 2.75 1.5
3/2 3.875 5.75 3 1
2 9 10.25 4.5 1
The Interpolation formula is
f(x) = f(x0) + (x - x0) f(x0 , x1 ) + (x - x0 )(x - x1 )f (x0 , x1 , x2 ) + ............ .......(1)
(i)
f(1/4) = f(0.25) = - 1 + (0.25 - 0)(1.25) + (0.25 - 0) (0.25 - 0.5) (1.5)
+ (0.25 - 0) (0.25 - 0.5)(0.25 - ...
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