Lecture 11.
Partial pivoting and lots of
demos.
Most of you already know that you when
doing Gaussian elimination one swaps rows in order to avoid a pivot whose
value is zero. When we encounter such a zero pivot we exchange rows to get a
non-zero in the pivot position. This exchange of rows is called pivoting.
Once floating point error is factored in, it's not only zero pivots that are
problematic, but any pivot whose magnitude is very small may cause an
unacceptable floating point rounding error. For this reason we use Gaussian
elimination along with a technique called partial pivoting. I motivated
this practice by giving a small problem where the use of partial pivoting made a
dramatic difference in
accuracy.
We then moved to the
computer where I demonstrated some of the m-files given by the authors Moler,
and Recktenwald.
The demos I
demonstrated this morning
were:
From Recktenwald: GEshow,
GEPivShow, luNopiv, and lupiv
From
Moler: lugui, and pivotgolf.
Posted: Thu - October 6, 2005 at 10:01 AM