Homework 2 - Nonlinear Equations

Due: Wednesday, September 19, 2001

Reading: Gerald and Wheatley, 6th edition, Chapter 1

Topics

1. bisection
2. linear interpolation
3. Newton's method
4. Muller's method
5. fixed point interation
6. methods for polynomials, multiple roots, error analysis, hybrid methods

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The following problems are on page 100ff of the text:

1. 1, 5 - graph using Maple
2. 11, also try starting at x=0 - what happens?
3. 23 and then 28
4. 29, 54, 59
5. 70 - use Maple

Sample Exam Question

For homework problems (unless text gives different instructions) and exams, you are required to use exam precision: chop to 4 significant digits only when you write an intermediate or final answer down and continue the calculations with those recorded numbers.

1. Find the root of f(x)=exp(x)-3/x using the secant method for 2 iterations beyond the starting guesses, x(1)=1.0 and x(2)=2.0. Record your answers in a table of k, x(k), x(k-1), f(x(k)), f(x(k-1)) for each interation k. (final answer = root=(4c) 1.049).

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