MCS 471 Computer Project 2
Due: Friday September 21,
2001 in class.
Problems turned in late (i.e. not in class) will be penalized 10% per day.
Write a well-documented Maple (or you may use some other language) program
that implements a hybrid root finding algorithm based on bisection and the
secant method as described in this …
Hand-out (in pdf format- you need Adobe Acrobat Viewer)
or Hand-out (in PostScript - you need Ghostview) see here for ghostview help.
You should set the digits in Maple to 6 and use a tolerence of 2.e-6. or use
single precision arithmatic.
Your program should print a table (including the starting point) of the form:
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 Maple's root finder fsolve.
- F1(x) = exp(-100.0*x) -
- 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 - 0.00001 Note: you should
know in advance from cp1 that you can not do this problem. After you have
determined that, please do the problem (x-1)**8 - 0.00001.
- Consider p(x) = 170.4*x^3 -
356.41*x^2 + 168.97*x + 18.601 which 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 these are simple zeros, but are
close together. You will need to increase the number of digits that Maple
uses to actually find them, or if you are using C you will need to use