Notes on Homework 3

1.  Show your code!  If you look in the Asaithambi, there is pseudocode for both the original LU decomposition and LU with scaled partial pivoting.

 

I will try to have the solution to problem 10 from the last homework up by Tuesday or copies available in the SIAM lounge so that you can see a copy of it to alter it for this problem.

 

2.  There are probably hints for this in your text.

 

3.  Show the code—please remember, however, that I have to look through 20 different codes for this, so annotating your code would be VERY appreciated!

 

4.  These two statements are very common theorems, which means there may be hints to solutions in your textbook.

 

5.  Dr. Noble told a student that the correct statement should be:

            Let A be a nonsingular n x n matrix, and let ||^.||_v denote a vector norm.  Show that ||x||_* = ||Ax||_v defines a vector norm (NOT matrix norm as on the original copy of the homework).

 

6.  Determining if it converges will probably be done by hand—or, actually, you can use Matlab.  If you determine it will converge, again, show your code.