4. For given function y = e*/(x3 + 1) and points on this function (0,1), (0.5,1.46553), (1,), find i) Linear spline interpolation ii) Quadratic spline interpolation iii) Cubic spline interpolation. iv) Plot all polynomials and exact function in a same figure. v) Pick up 100 points between (0,1) and calculate root mean square error between true values and values obtained from i), ii), iii) polynomials.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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4. For given function y = e*/(x³ + 1) and points on this function (0,1), (0.5,1.46553), (1,5), find
i) Linear spline interpolation
ii) Quadratic spline interpolation
iii) Cubic spline interpolation.
iv) Plot all polynomials and exact function in a same figure.
v) Pick up 100 points between (0,1) and calculate root mean square error between true values
and values obtained from i), ii), iii) polynomials.
Transcribed Image Text:4. For given function y = e*/(x³ + 1) and points on this function (0,1), (0.5,1.46553), (1,5), find i) Linear spline interpolation ii) Quadratic spline interpolation iii) Cubic spline interpolation. iv) Plot all polynomials and exact function in a same figure. v) Pick up 100 points between (0,1) and calculate root mean square error between true values and values obtained from i), ii), iii) polynomials.
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