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Mth510Asgt3Solutions_W05

# Mth510Asgt3Solutions_W05 - Mathematics 510 Winter 2005...

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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 j-1.0-1.0 1-0.96-0.151 2-0.86 0.894 3-0.79 0.986 4 0.22 0.895 5 0.5 0.5 6 0.93-0.306 (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 6-th 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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Mth510Asgt3Solutions_W05 - Mathematics 510 Winter 2005...

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