Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
Exact Tests For Singular Network Data, Ian H. Dinwoodie, Kruti Pandya
Exact Tests For Singular Network Data, Ian H. Dinwoodie, Kruti Pandya
Mathematics and Statistics Faculty Publications and Presentations
We propose methodology for exact statistical tests of hypotheses for models of network dynamics. The methodology formulates Markovian exponential families, then uses sequential importance sampling to compute expectations within basins of attraction and within level sets of a sufficient statistic for an over-dispersion model. Comparisons of hypotheses can be done conditional on basins of attraction. Examples are presented.
Convergence Rates Of The Dpg Method With Reduced Test Space Degree, Timaeus Bouma, Jay Gopalakrishnan, Ammar Harb
Convergence Rates Of The Dpg Method With Reduced Test Space Degree, Timaeus Bouma, Jay Gopalakrishnan, Ammar Harb
Mathematics and Statistics Faculty Publications and Presentations
This paper presents a duality theorem of the Aubin-Nitsche type for discontinuous Petrov Galerkin (DPG) methods. This explains the numerically observed higher convergence rates in weaker norms. Considering the specific example of the mild-weak (or primal) DPG method for the Laplace equation, two further results are obtained. First, the DPG method continues to be solvable even when the test space degree is reduced, provided it is odd. Second, a non-conforming method of analysis is developed to explain the numerically observed convergence rates for a test space of reduced degree
Dispersive And Dissipative Errors In The Dpg Method With Scaled Norms For Helmholtz Equation, Jay Gopalakrishnan, Ignacio Muga, Nicole Olivares
Dispersive And Dissipative Errors In The Dpg Method With Scaled Norms For Helmholtz Equation, Jay Gopalakrishnan, Ignacio Muga, Nicole Olivares
Mathematics and Statistics Faculty Publications and Presentations
This paper studies the discontinuous Petrov--Galerkin (DPG) method, where the test space is normed by a modified graph norm. The modification scales one of the terms in the graph norm by an arbitrary positive scaling parameter. The main finding is that as the parameter approaches zero, better results are obtained, under some circumstances, when the method is applied to the Helmholtz equation. The main tool used is a dispersion analysis on the multiple interacting stencils that form the DPG method. The analysis shows that the discrete wavenumbers of the method are complex, explaining the numerically observed artificial dissipation in the …