Math 221, Matrix Computations, Fall 2008.
 Class Information

General information. In particular, see this document
for what is to be covered in the class this semester
(updated Sept. 1, 2008.)
 Homework Sets

Homework Set #1, Due Sept. 3
Selected solutions . Here is a link to
George Forsythe's paper on solving quadratic equations
.

Homework Set #2, Due Sept. 10
Selected solutions .

Homework Set #3, Due Sept. 17
Selected solutions .

Homework Set #4, Due Sept. 24
Selected solutions .

Homework Set #5, Due Oct. 1

Homework Set #6, Due Oct. 13 Notice that it has been
updated (Oct. 3, 2008)
Selected solutions .

Homework Set #7, Due Oct. 20

Homework Set #8, Due Oct. 27

Homework Set #9, Due Nov. 3

Homework Set #10, Due Nov. 10

Homework Set #11, Due Nov. 17

Homework Set #12, Due Nov. 24

Homework Set #13, Due Dec. 1

Homework Set #14, Due Dec. 8
 Midterm Solutions and Sample Exams.
 Class Projects
 Here are the
class projects . We will start to have weekly
meetings on these projects next week (week of Oct. 27).
 Matlab codes

A stable way and
and unstable way to generate the Householder vectors.

quadroot.m is a matlab program to find the two roots
of a quadratic equation. However, it can easily overflow or
underflow for very large or very tiny inputs. This problem
can be much alleviated by

a simple modification involving a scaling trick.

bisect.m by Prof. J. Demmel.

pcg.m
is a matlab program implementing the preconditioned
conjugate gradient (pcg) method to solve linear system of
equations.

housetest.m
is a matlab program that tests the numerical stability of
two slightly different ways of computing the Householder
transformation.

Classicl GramSchmidt
and
modified GramSchmidt for computing QR
factorization.
 A simple
matlab code for computing quadratic roots in two
different ways, with its
modified version to reduce overflow/underflow
problems.
 Hager's Condition Estimator
hager.m . This version estimates the
1norm of a given matrix B. However, Hager's condition
estimator can sometimes fail badly. Run
counterexample_hager.m to see the results.
 Generalized Kahan Matrix as generated by
counterexample_GEPP.m. This matrix causes very large
element growth with GEPP.
 Here is
the Kahan Matrix. This one misses
tiny singular values in QR with column pivoting.
 Here is
the QR method. It can be used to drive one eigenvalue to
zero.
 Here is
SQR: the Symmetric QR method. It can be used to drive one eigenvalue to
zero.
 Here is
the Rayleigh Quotient Iteration method. It is usually
cubically convergent (to some unknown eigenvalue). But it
does not always converge.
 Here is
BiSVD: the dqds method for the bidiagonal SVD problem, without
shifts. It should always converge to the smallest singular
value.
 Pictures
 External Link
 Prof. Demmel has taught Math221 in the past, using his
own text. See Demmel's
Math 221 Website. Among other things, there is an
errata of the text book, as well as a number of
relevant matlab
codes.