BibTeX
@ARTICLE{
Pryce2010Con,
author = "Pryce, J. D. and Khoshsiar Ghaziani, R. and De Witte, V. and Govaerts, W.",
title = "Computation of normal form coefficients of cycle bifurcations of maps by algorithmic
differentiation",
journal = "Mathematics and Computers in Simulation",
issue_date = "September, 2010",
volume = "81",
number = "1",
month = "sep",
year = "2010",
issn = "03784754",
pages = "109119",
numpages = "11",
url = "http://dx.doi.org/10.1016/j.matcom.2010.07.014",
doi = "10.1016/j.matcom.2010.07.014",
acmid = "1857366",
publisher = "Elsevier Science Publishers B. V.",
address = "Amsterdam, The Netherlands, The Netherlands",
keywords = "Bifurcation, Iterated map, Matlab, Multilinear form, Taylor series",
abstract = "As an alternative to symbolic differentiation (SD) and finite differences (FD) for
computing partial derivatives, we have implemented algorithmic differentiation (AD) techniques into
the Matlab bifurcation software Cl_MatcontM, http://sourceforge.net/projects/matcont, where we need
to compute derivatives of an iterated map, with respect to state variables. We use derivatives up to
the fifth order, of the iteration of a map to arbitrary order. The multilinear forms are needed to
compute the normal form coefficients of codimension1 and 2 bifurcation points. Methods based on
finite differences are inaccurate for such computations. Computation of the normal form coefficients
confirms that AD is as accurate as SD. Moreover, elapsed time in computations using AD grows
linearly with the iteration number J, but more like Jd for d th derivatives with SD. For small J, SD
is still faster than AD.",
ad_tools = "CL_MatContM",
ad_theotech = "Taylor Arithmetic"
}
