AMSC 607 / CMSC 764 Homework 1, Fall 2006
Due Thursday September 28, 2006, 2pm
Assignment: Solve Problem 10.16, p.340 (the 106th page of the pdf file). (In
my hard-copy of the book, it is Problem 16, p.327.) It begins, “Write a computer
program for minimizing a multivariate function....”
Changes:
•Use the Gerschgorin Theorem to determine a parameter delta so that the
smallest eigenvalue of H+δIis at least 10−2kHk∞. Then compute the
Cholesky factors of H+δI.
•Use cvsrch (see website) as your backtracking line search.
Notes:
•Your implementation of Newton’s method should be in a function newtonmin
which can be easily applied to other functions f(x) with x∈ Rnand n
arbitrary.
•The function newtonmin should be well-documented, as if it were a library
code. In particular, documentation at the top of the function should
include:
–purpose of code, since this is certainly the first thing a user wants to
know!
–name of author, since it provides someone to whom bugs can be
reported and questions asked.
–date of the original code and a list of later modifications, since it
gives information such as whether the code is likely to run under
the current computer environment and whether it might include the
latest advances.
–description of each input parameter, so that a user knows what in-
formation needs to be provided and in what format.
–description of each output parameter, so that a user knows what
information will be yielded.
–brief description of the method and references, to help a user decide
whether the method fits his/her needs.
In-line documentation should identify the major sections of the code and
provide some detail on the method used. It is important in specifying the
algorithm, identifying bugs, and providing information to someone who
might need to modify the software in order to solve a slightly different
problem.
Note that the documentation should be an integral part of the code; in
other words, it is not enough to include it in a separate document, because
a potential user might not have access to that document.
1
