Homework 2 - Nonlinear Equations

Due: Wednesday, September 19, 2001

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

  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

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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