Math 471 Computer Project 1

Due: Friday Feb 11 in class.

Problems turned in late (i.e. not in class) will be penalized 10% per day.

Write a well-documented Matlab function (m-file) that implements a hybrid root finding algorithm based on bisection and the secant method as described in class and in the supplement. You should set the default arithmetic in Matlab and use a tolerance of .5e-10 in the stopping criteria.

Your program should display the following table including the starting point: 

K   X(K)     ABS(X(K)-X(K-1))      F(X(K))
Test Examples: For each of the examples, use (1,2) as the initial sign change interval (double check this of course). You should compare your answers with the roots found using Matlab's root finder fzero.
  1. F1(X) = exp(-4.5*X) -X/200.
  2. F2(X) = X^8 - 8*X^7 + 28*X^6 - 56*X^5 + 70*X^4 - 56*X^3 + 28*X^2 - 8*X + 1 - 1e-14 Note: you should know in advance from computer problem 0 that you can not do this problem. Use fplot over the interval [.99,1.03] to illustrate the problem. After you have determined that, please do the problem (x-1)**8 - 1e-14
  3. p(x) = 170.4*x^3 - 356.41*x^2 + 168.97*x + 18.601 has three real zeros. The two positive zeros lie in the interval [1.091607 , 1.091608 ] can you find them with any accuracy? You may want to try using some of the techniques mentioned in class for finding zeros located near each other. Note that these are simple zeros, but are close together.

You should submit your Matlab function along with a separate sheets for each of the above examples. For the examples, you should use your function and Matlab's fzero as a comparison. The diary command might be useful.

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