MATH 521 Additional Online Reading List
Prof. Zachariah B. Etienne
Note 1: All links to Wikipedia reference versions of the article
that have been vetted by the instructor, and may be considered trustworthy.
Note 2: This reading list should be considered as a
complement to the lecture notes as well as the suggested text for
this course: (Numerical Recipes, second edition or
higher)
Preliminaries:
All material in MATH 521 builds on basic undergraduate
mathematics, and when you start this course, I assume you are
already well-versed in undergraduate mathematics.
If you need to brush up, here are some resources that may
help:
Tips for determining how many digits of
significance you can expect from a double-precision calculation (note
that this
neglects guard
digits):
Evaluating the expression according to proper order-of-operation,
check for arithmetic steps that go out of bounds for double precision
arithmetic. (Note that the smallest nonzero number is roughly plus or minus
1e-308; largest non-infinite number is roughly plus or minus
1e+308). If this happens, evaluate to zero or infinity as appropriate. You might still
retain some digits of significance.
Check for catastrophic cancellation.
Check for numbers that are exactly representable by double
precision (generally the number zero or powers of 2). If these exist, they are
known to an infinite number of significant digits. If not, they are
generally known to only 15--16 significant digits.
Dividing two numbers that are identical to all significant digits
will yield one exactly.
Subtracting two numbers that are identical to all significant digits
will yield zero exactly.
Please contact the instructor if you would like to contribute further tips.