Performance Analysis
of Numerical Software for
Stiff Ordinary
Differential Equations Prof.
Roger Alexander , Jangwoon Lee, Omar Chilous, Sylvia Fanous,
Nathan
Ray
The purpose of this project is to apply a new method to evaluate the
performance of numerical solvers of stiff ordinary differential
equations. We evaluate the performance of the numerical software by
comparing computed solutions with analytic approximations obtained
by the method of matched asymptotic expansions.
Rational realization of nonzero rational
eigenvalues for
trees and symmetric tree sign patterns Prof.
Leslie Hogben, Rana Mikkelson, Atoshi Chowdhury, Jude Melancon
A sign pattern is a matrix whose entries are
elements of {+, -,0}; it describes the set of real matrices whose
entries
have the signs in the pattern. A graph (that allows loops but not
multiple
edges) describes the set of symmetric matrices having a
zero-nonzero
pattern of entries determined by the absence or presence of edges
in the graph. DeAlba, Hardy, Hentzel, Hogben Wangsness gave algorithms
for the computation of maximum multiplicity and minimum rank of
matrices
associated with a tree sign pattern or tree, and an algorithm to obtain
an integer matrix realizing minimum rank. We extend these results
by giving algorithms to obtain a
symmetric rational matrix realizing the maximum multiplicity of a
rational
eigenvalue among symmetric matrices associated with a symmetric tree
sign pattern or tree. The group's
paper
has
appeared in
Linear Algebra and Its
Applications.
Iowa
State University Combinatorial Matrix Theory Research Group