Math 464A, Numerical Analysis, Fall, 2015
This is the Math 464A homepage. Consult it from time to time to find
useful information for the course. I will include links to the syllabus and
other course information.
Here is a copy of current course information.
- (12/10/15) Sample problems for the final.
- (10/22/15) Sample problems for the midterm.
- (10/1/15) Nonsingularity A proof that Ax=b is uniquely
solvable (in the square case) exactly when Ax=0 implies x=0.
- (9/14/15) Least squares and normal
- (9/14/15) A discussion of the Cholesky factorization.
- (9/14/15) One of the books I recommended has disappeared from the
library. But you can link to the ebook version
Numerical Computing with IEEE Floating Point Arithmetic
by Michael Overton.
- (9/14/15) Wolfram Alpha is a handy free
online tool that you might find useful.
- (9/14/15) Some of you have asked about other numerical analysis books.
Elementary Numerical Analysis by Conte and DeBoor is a good
numerical analysis reference book. It's
on course reserve.
- (9/14/15) Two documents on norms.
norms and norms2
- (9/14/15) Scanned images of homework from section 2.1 and section 2.2
- (9/14/15 Some of you do not yet have a copy of the text. Here is Scan of the first few pages.
- (9/14/15) Notes on Singular Value Decomposition.
- (9/14/15) Carl DeBoor on divided differences.
- (9/14/15) Class email address is email@example.com
- (9/14/15) Least squares applied to
- (9/14/15) A discussion of Cauchy sequences can be found in
Taylor's book or Folland's book; and also on page 197 of Johnson
and Riess. There is a discussion of Newton's method in several
variables and Cauchy sequences on pages 194-198 of Johnson and
Riess. There will be no problems involving Cauchy sequences on
- (9/14/15) Wikipedia has an entry on Taylor's theorem, with a
statement and proof of the several variable case. It is also
stated and proved in most books on advanced calculus such as the
books by Gerald Folland and Angus Taylor (not Brook Taylor, for
whom the theorem is named). These books are both titled
- (9/14/15) A proof of the formula for a sum of powers is in Bernoulli Numbers and the Riemann Zeta Function by B. Sury.
- (9/14/15) What Every Computer Scientist Should Know About Floating-Point Arithmetic
- (9/14/15) A quote from Richard Hamming: "The purpose of numerical
analysis is insight, not numbers."
- (9/14/15) SAGE website.
- (9/14/15) Syllabus