Math 344 - Numerical Methods II - MatLab Assignment 1

MatLab Assignment 2 -- Turn in on Feb. 9

Write a MatLab m-function which implements Jacobi Method for solving systems of linear equations Ax=b with the following input and output.

  Input  - A, b, x⁽⁰⁾ (initial iteration) 
           n (# of unknowns), epsilon, k_max (# of iterations < k_max)
  Output - k (# of iterations), x^(k) (||x^(k)-x^(k-1)|| < epsilon)

Write a MatLab m-function which implements Gauss-Seidel Method for solving systems of linear equations Ax=b with the following input and output.

  Input  - A, b, x⁽⁰⁾ (initial iteration) 
           n (# of unknowns), epsilon, k_max (# of iterations < k_max)
  Output - k (# of iterations), x^(k) (||x^(k)-x^(k-1)|| < epsilon)

Use your programs to solve the following problems.
Page 230: #1(b), #2(d), #4
Page 240: #1(b), #2(d), #4
These 3 problems are the same on both pages. Use two methods to solve them to see which method is better in general. Do verify first that the methods converge for these problems.