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Unformatted text preview: Mathematics 510 Winter 2005 Problem Set 3 Due: Monday April 11, in class. Notes: See assignment 1 for guidelines regarding all homework sets. Problems: 1. Consider the data points j x j y j1.01.0 10.960.151 20.86 0.894 30.79 0.986 4 0.22 0.895 5 0.5 0.5 6 0.930.306 (a) Plot these points on a graph and draw, by hand, the curve you think best fits this data. (b) Use the method of divided differences to find the unique polynomial of degree 6 which interpolates the data. Record your polynomial in the proper form. We round the coefficients to get P ( x ) = 1 . 0 + 21 . 225( x + 1) + 76 . 694( x + 1)( x + 0 . 96) + 110 . 594( x + 1)( x + 0 . 96)( x + 0 . 86) + 54 . 225( x + 1)( x + 0 . 96)( x + 0 . 86)( x + 0 . 79) + 15 . 951( x + 1)( x + 0 . 96)( x + 0 . 86)( x + 0 . 79)( x . 22) + . 0436500( x + 1)( x + 0 . 96)( x + 0 . 86)( x + 0 . 79)( x . 22)( x . 5) (c) Graph the polynomial in (1b) and compare with the results in (1a). Write a conclusion based on your work in (1a) and (1b). We compare and find that the 6th degree polynomial oscillates quite more than we might expect (d) Find the free cubic spline which interpolates these data. Record your answer carefully, displaying the coeffi cents in an orderly way. Plot a graph of your cubic spline. There is more than one way to do this. We used Maple and got 21 . 51547262 + 22 . 51547262 v 806...
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 Fall '09
 MEOW
 Numerical Analysis, Sets, Quadratic equation, Degree of a polynomial, Polynomial interpolation, Gaussian quadrature

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