Homework 2 - Nonlinear Equations

Due:

Reading: Sauer, Numerical Analysis, Chapter 1

Topics
  1. bisection
  2. fixed point interation
  3. secant method
  4. Newton's method
  5. Muller's method
  6. methods for polynomials, multiple roots, error analysis, hybrid methods
  • Section 1.1: Exercises - 3c (exam precision); Computer Problems - 3b, 4b (exam precision and Matlab)
  • Section 1.2: Exercises - 1,3,7; Computer Problems - 1b, 3b
  • Section 1.3: Exercises - 1,3,4;
  • Section 1.4: Exercises - 1a,b, 3a, 5,9; Computer Problems - 2b
  • Section 1.5: Exercises - 1b, 4
    Sample Exam Question
    For homework problems (unless text gives different instructions) and exams, you are required to use exam precision: round 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).

    by Charles Tier