BAP: Lecture 4 (Feb 21, 2002)

The notes for this lecture are available in
In this lecture, we saw the need for partial or complete pivoting in Gaussian elimination. We then examined cases in which pivoting is not necessary. They included: We then began an examination of the smoothed analysis of the growth factors of Gaussian elimination without pivoting.
For this class's matlab example, you need the program noPivot.m, which produces the LU factorization without pivoting. Today's matlab example follows. Try it out yourself. Get the code you need at the BAP matlab code directory.
A = [2^(-50), 1; 1, 1];
[l,u] = noPivot(A);
Now, if we go machine epsilon, which is
we get
A = [2^(-55), 1; 1, 1];
[l,u] = noPivot(A);