Problem Sheet on Interpolation
Q -1. Find y(3.2) from the following data:
x : 0 1 2 3 4 5
y: 0 1 14 51 124 245
using:
(a) Gregory – Newton Forward Difference interpolation Formula
(b) Gregory – Newton Backward Difference interpolation Formula
(c) Lagrange Interpolation Formula
(d) Newton’s Divided Difference interpolation Formula
Comment on the accuracy of your results.
Q -2. Make Lagrange Polynomial for the data:
(xi , yi) = (-2, 0), (0, 2), (1, 0), (2, 4)
and hence find: y (1.1), y (2.1), y (2.5)
Comment on the error involved in these interpolated values
Q -3. Using a suitable interpolation formula, find
(2.3) from the data
x : 0 1 4 5
(x): 0 0.25 16 31.25
Q -4. What is the degree of the interpolation polynomial for the data
(1, 5), (2, 18), (3, 37), (4, 62), (5, 93)
Q -5. The following table gives pressure of a steam at a given temperature. Using
Newton’s formula, compute the pressure for a temperature of 142oC.
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Temperature, oC 140 150 160 170 180
Pressure, kgf/cm2 3.685 4.854 6.302 8.076 10.225
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Q -6. Find Newton’s backward interpolating polynomial for the following data:
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x 1 2 3 4 5
y 1 -1 1 -1 1
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