assignment_5[1]

assignment_5[1] - What is the best fit function, and what...

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Math 400 Assignment #5 Approximation Theory 1. 2. ( 29 1 0 for 1 2 1 1 1 for 2 2 1 0 for 1 2 x f x x x - ≤ ≤ - = - < < 3. 0.0 0.2 0.5 0.7 1.1 1.5 1.9 2.3 2.8 3.1 102.56 113.18 130.11 142.05 167.53 195.14 224.87 256.73 299.50 326.72 i x i y Find the least squares polynomials of degrees 1, 2, 3, and 4 for the data: In each case compute E , the sum of the squared errors, and provide a graph of the data and the best fit polynomial. Which polynomial would you use to represent the data? Why? For the data in Problem 1, derive the normal equations for the least squares approximation of the form . Solve the nonlinear system of two equations in the unknowns a and b numerically using Newton’s method.
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Unformatted text preview: What is the best fit function, and what is the value of E , the sum of the squared errors, when using it? Provide a graph of the data and of the fitting function. For the function find the best fit polynomial, in the least squares sense, of degrees 0 through 4. Use the orthogonal family of Legendre polynomials rather than the usual power function basis. Provide one graph showing f and the five approximating polynomials. 1 , cos , cos2 , cos3 , cos4 , cos5 . 2 x x x x x 4. Repeat exercise 3. using trigonometric functions with the basis functions: ( 29 a x f x be = Due: May 20, 2010...
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