Multiple Weighted Regression Analysis of the Curvature of a 3D Brane in a 4D Bulk Space under a Homogenous Vector Field
by Stefan von Weber and Alexander von Eye
Weighted multiple regression analysis is shown to be a suitable tool for finding the normal vector of an inclined space. The outer vector product is defined only in the 3-dimensional space. The use of that vector product in a space with more than three dimensions requires an extension to higher dimensions. Both methods, regression analysis and generalization of the outer vector product, use the cross-product of matrices, and are mathematically similar. However, using weighted multiple regression analysis comes with the advantage that one can perform two tasks at the same time: (1) finding the normal vector of the locally fitted hyperplane, and (2) averaging over distributed loads. Application of multiple weighted regression is suggested when modelling stochastically distorted surfaces, to obtain local fit of a plane to a curved surface, in particular in higher dimensional spaces. The example from mechanics presented in this paper belongs to this class of models.
Multiple weighted regression, normal vector, curved surfaces, elastic membrane
Stefan von Weber, email@example.com
Alexander von Eye, firstname.lastname@example.org
Graf, R. G., email@example.com
READING THE ARTICLE: You can read the article in
portable document (.pdf) format (644293 bytes.)
NOTE: The content of this article is the intellectual property of the authors, who retains all rights to future publication.
This page has been accessed 2521 times since JULY 13, 2010.
Return to the Home Page.