Homework 2 - Nonlinear Equations

Due: Wednesday, February 2, 2000

Reading: Gerald and Wheatley, 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
The following problems are on page 100 of the text. You should write Matlab code for each of the methods, e.g bisection, etc.

  1. 1 - also graph using Matlab
  2. 5 - do this using Matlab and by hand using exam precision, i.e. 4 digit chop. Compare the results.
  3. 11, also try starting at x=0 - what happens?, 18, 22b
  4. 23 and then 28
  5. 29, 54, 59
  6. 70
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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