5,125 research outputs found
Quadratic distances on probabilities: A unified foundation
This work builds a unified framework for the study of quadratic form distance
measures as they are used in assessing the goodness of fit of models. Many
important procedures have this structure, but the theory for these methods is
dispersed and incomplete. Central to the statistical analysis of these
distances is the spectral decomposition of the kernel that generates the
distance. We show how this determines the limiting distribution of natural
goodness-of-fit tests. Additionally, we develop a new notion, the spectral
degrees of freedom of the test, based on this decomposition. The degrees of
freedom are easy to compute and estimate, and can be used as a guide in the
construction of useful procedures in this class.Comment: Published in at http://dx.doi.org/10.1214/009053607000000956 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A Semismooth Newton Method for Tensor Eigenvalue Complementarity Problem
In this paper, we consider the tensor eigenvalue complementarity problem
which is closely related to the optimality conditions for polynomial
optimization, as well as a class of differential inclusions with nonconvex
processes. By introducing an NCP-function, we reformulate the tensor eigenvalue
complementarity problem as a system of nonlinear equations. We show that this
function is strongly semismooth but not differentiable, in which case the
classical smoothing methods cannot apply. Furthermore, we propose a damped
semismooth Newton method for tensor eigenvalue complementarity problem. A new
procedure to evaluate an element of the generalized Jocobian is given, which
turns out to be an element of the B-subdifferential under mild assumptions. As
a result, the convergence of the damped semismooth Newton method is guaranteed
by existing results. The numerical experiments also show that our method is
efficient and promising
Unified control/structure design and modeling research
To demonstrate the applicability of the control theory for distributed systems to large flexible space structures, research was focused on a model of a space antenna which consists of a rigid hub, flexible ribs, and a mesh reflecting surface. The space antenna model used is discussed along with the finite element approximation of the distributed model. The basic control problem is to design an optimal or near-optimal compensator to suppress the linear vibrations and rigid-body displacements of the structure. The application of an infinite dimensional Linear Quadratic Gaussian (LQG) control theory to flexible structure is discussed. Two basic approaches for robustness enhancement were investigated: loop transfer recovery and sensitivity optimization. A third approach synthesized from elements of these two basic approaches is currently under development. The control driven finite element approximation of flexible structures is discussed. Three sets of finite element basic vectors for computing functional control gains are compared. The possibility of constructing a finite element scheme to approximate the infinite dimensional Hamiltonian system directly, instead of indirectly is discussed
A new approach to the study of quasi-normal modes of rotating stars
We propose a new method to study the quasi-normal modes of rotating
relativistic stars. Oscillations are treated as perturbations in the frequency
domain of the stationary, axisymmetric background describing a rotating star.
The perturbed quantities are expanded in circular harmonics, and the resulting
2D-equations they satisfy are integrated using spectral methods in the
(r,theta)-plane. The asymptotic conditions at infinity, needed to find the mode
frequencies, are implemented by generalizing the standing wave boundary
condition commonly used in the non rotating case. As a test, the method is
applied to find the quasi-normal mode frequencies of a slowly rotating star.Comment: 24 pages, 7 figures, submitted to Phys. Rev.
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