Homework 3 - Systems of Equations

Topics

1. Direct Methods
   1. Gaussian elimination method-partial pivoting, etc.
   2. LU decomposition - derived from Gaussian elimination
2. norms and condition numbers
3. Indirect (iterative) Methods
   1. Jacobi
   2. Gauss-Seidel
   3. Eigenvalue problems
4. Systems of Nonliner equations

Part A:

1. 2.1: 1b; 3a; 5 (use Matlab to check solutions)
2. 2.2: 1b; 2a; 3a; 5 (use Matlab to check solutions)
3. 2.3: 1; 2b; 3a,e; 5; computer problem 3 use Matlab's backlash command.
4. 2.4: 1b; 2c; 3b; 5

Part B:

1. 2.5: 1a,c; 2a,b; computer problem 1; use Matlab to find the approximate solution of 1c after 2, 10 and 20 steps. Compare with Matlab's direct solution.
2. 2.7: 1a,b; 2a; 3b; 4
3. Power method 12.1: 1a; 3b; 5ac; 9