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. 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.
Example problems:
When the following expressions are evaluated by the computer,
to how many significant decimal digits will the numerical result
agree with the exact result? In computing the "exact result", you
are to assume all numbers given are valid to infinitely many
significant digits. E.g., 2.15 = 2.1500000000..... In computing the
``numerical result'', you are to assume that unless otherwise
specified (e.g., ``1 is exact''), each number written
below can be represented to only 16 significant digits, and that
IEEE 754 standard-compliant double precision arithmetic is applied.
We use computer scientific notation, such that, e.g.,
5.63e12 = 5.63 x 1012.
Your answer will consist of a single number (infinity
is an acceptable number), and answers will be accepted so long as
they are correct within 1 decimal digit.