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HW8 - polyfit to determine the cubic polynomial...

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HOMEWORK ASSIGNMENT 8 EGM 3344 Regression and Interpolation Concepts Due: Wednesday, November 17, 2010 Problems from Chapra book chapters 14 through 15 For all of these problems, feel free to use a simple Matlab program to calculate function values (like using a calculator) when the indicated approach is by hand. For problems in Chapter 15, you will frequently need to choose the best points to use for fitting a polynomial of specified degree. For example, if you are given 5 points ( x , y ) and asked to fit a cubic polynomial, you should chose the 4 points whose x values are closest to the value at which the interpolated result y is desired. Problem Approach Comments 14.3 Matlab Do not worry about calculating / y x s . 14.6 Matlab Perform the fit using the model 0 1 2 o a a T a c = + + . 14.7 Matlab 14.14 Matlab Calculate 2 r values using the untransformed data to justify which of the four curve fits is the “best.” 15.2 Hand Create a divided difference table to help solve the problem. 15.3 Hand 15.5 Matlab Use the built-in Matlab function

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Unformatted text preview: polyfit to determine the cubic polynomial coefficients. Use the bisection algorithm from one of your old homework assignments to solve the rootfinding problem. Answers 14.3 2 3 11.4887 7.143817 1.04121 0.046676 y x x x = -+-+ 2 0.829 r = 2 14.6 13.52214286 0.20123810 0.10492857 o T c =--At T = 12 and c = 15, the predicted value of o is 9.53335714 Percent relative error = 4.8774% 14.7 2 3 14.027143 0.336423 0.00574444 0.000043704 0.10492857 o T T T c =-+--At T = 12 and c = 15, the predicted value of o is 9.16781492 which is much closer to the true value of 9.09 than the result in the previous problem. 14.14 a) Linear model 3 b) Power model Wrong R^2 values for b) – should be 0.9377. c) Saturation-growth rate model d) Quadratic model 15.2 First order: 12.5 Second order: 10.5 Third order: 10 Fourth order: 10 15.3 4 First order: 12.5 Second order: 10.5 Third order: 10 15.5 3 2 ( ) 0.15 1.5 5.25 7.5 f x x x x = -+-+ x = 2.2156...
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