Numerical Mathematics Problems (Matlab)

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avav3535

Mathematics

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There are 4 problems. The answer should include Matlab code. 


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2. Find the polynomial of degree 10 that interpolates the function arctan x at 11 equally spaced points in the interval [1, 6]. Print the coefficients in the Newton form of the polynomial. Compute and print the difference between the polynomial and the function at 33 equally spaced points in the interval [0, 8]. What conclusion can be drawn? 6. Write routines analogous to Coef and Eval using the Lagrange form of the interpolation polynomial. Test on the example given in this section at 20 points with h/2. Does the Lagrange form have any advantage over the Newton form? 11. Use mathematical software such as Matlab, Maple, or Mathematica to find an interpo- lation polynomial for the points (0,0), (1, 1), (2, 2.001), (3, 3), (4,4), (5,5). Evaluate the polynomial at the point x = 14 or x = 20 to show that slight roundoff errors in the data can lead to suspicious results in extrapolation. 8(x) = 17. (Padé interpolation) Find a rational function of the form a+bx 1+cx that interpolates the function f(x) = arctan (x) at the points Xo = 1, x1 = 2, and x2 = 3. On the same axes, plot the graphs of f and g, using dashed and dotted lines, respectively.
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