can in general only be found by an iterative process in which successively better, in some sense, approximations to the solution are computed. Of the methods available most rely on evaluating at each stage of the calculation a set of residuals and from these obtaining a correction to each element of the approximate solution. The most common way of doing this is to take each correction to be a s...

Historical Development of the BFGS Secant Method and Its Characterization Properties by Joanna Maria Papakonstantinou The BFGS secant method is the preferred secant method for finite-dimensional unconstrained optimization. The first part of this research consists of recounting the historical development of secant methods in general and the BFGS secant method in particular. Many people believe t...

In this paper, we propose a natural way to extend a bivariate Powell–Sabin (PS) B-spline basis on a planar polygonal domain to a PS B-spline basis defined on a subset of the unit sphere in R3. The spherical basis inherits many properties of the bivariate basis such as local support, the partition of unity property and stability. This allows us to construct a C1 continuous hierarchical basis on ...

This paper reports the study results on neural network training algorithm of numerical optimization techniques multiface detection in static images. The training algorithms involved are scale gradient conjugate backpropagation, conjugate gradient backpropagation with Polak-Riebre updates, conjugate gradient backpropagation with Fletcher-Reeves updates, one secant backpropagation and resilent ba...

Approximately 1 in 6 children in the United States are diagnosed with one or more developmental disabilities or delays (Boyle et al., 2011). Although the number of therapeutic approaches for children with developmental disabilities has increased, no single treatment or combination of treatments is effective in relieving symptoms for all individuals (Scharoun, Reinders, Bryden & Fletcher, 2014)....

This paper reports work done to improve the modeling of complex processes when only small experimental data sets are available. Neural networks are used to capture the nonlinear underlying phenomena contained in the data set and to partly eliminate the burden of having to specify completely the structure of the model. Two different types of neural networks were used for the application of pulpi...

Studies on the response of the blackfly Simulium ornatum s.l (Diptera Simuliidae) to carbon dioxide (CO2), acetone, 1-octen-3-ol and air was conducted in the laboratory using a Y-tube olfactometer. The blackflies were found to exhibit a high degree of activity in the olfactometer and responded to the various odours. The results showed that CO2 and l-octen-3-ol were attractive to the flies at lo...

Recovery of common agricultural weeds after burial by soil was studied in four greenhouse and three field experiments. Species studied included velvetleaf, Powell amaranth, common lambsquarters, barnyardgrass, and giant foxtail. Seedlings were bent over before burial to simulate the effect of the impact of soil thrown by a cultivator. Altogether, more than 35,000 seedlings were marked and obser...

It is observed that the Powell-Sabin 12-split triangle is reen-able since the same split of the 4 similar subtriangles of a triangle contains the lines of split of the original triangle. This property of the split is the key to the existence of a subdivision scheme, for the evaluation of the C 1 quadratic spline on the split which interpolates function and gradient values at the 3 vertices of t...

Incorporating computers into daily K-12 classroom teaching promises to benefit student learning, and improve teaching practice substantially. Computer enhanced curricula may enable more teachers to create exploratory and inquiry based lessons, but in most cases supporting software have only been realized as practice tools for specific rote learning skills. Drills do little to help students deve...