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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.

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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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