Recently, important contributions on convergence studies of conjugate gradient methods have been made by Gilbert and Nocedal [6]. They introduce a “sufficient descent condition” to establish global convergence results, whereas this condition is not needed in the convergence analyses of Newton and quasi-Newton methods, [6] hints that the sufficient descent condition, which was enforced by their ...

This chapter focuses on comparing the forecasting ability of the backpropagation neural network (BPNN) and the nonlinear autoregressive moving average with exogenous inputs (NARX) network trained with different algorithms; namely the quasi-Newton (Broyden-Fletcher-Goldfarb-Shanno, BFGS), conjugate gradient (Fletcher-Reeves update, Polak-Ribiére update, Powell-Beale restart), and Levenberg-Marqu...

Language can be approached from many different vantage points – neuroanatomy, psychology, phonetics, hearing, vision, physics, information theory, formal logic, and so on. Most scientific and linguistic accounts have focused on defining units of analysis, such as the phoneme, the word, and the phrase. Some of the more ingenious, such as Articulation Theory (Fletcher and Galt, 1940; French and S...

A trust-region SQP-filter algorithm of the type introduced by Fletcher and Leyffer [Math. Program., 91 (2002), pp. 239–269] that decomposes the step into its normal and tangential components allows for an approximate solution of the quadratic subproblem and incorporates the safeguarding tests described in Fletcher, Leyffer, and Toint [On the Global Convergence of an SLPFilter Algorithm, Technic...

A new and practical approach to computer-aided design optimization is presented. Central to the process is the application of least pth approximation using extremely large values of p, typically 1000 to 1000000. It is shown how suitable and reasonably wellconditioned objective functions can be f ornndated, giving particular emphasis to more generaf approximation problems as, for example, in fil...

Authors Kelly J. Butnor, MD, FCAP* Department of Pathology and Laboratory Medicine, Fletcher Allen Health Care/University of Vermont, Burlington, Vermont Mary Beth Beasley, MD, FCAP Department of Pathology, Mt. Sinai Medical Center, New York, New York Philip T. Cagle, MD, FCAP Department of Pathology, The Methodist Hospital, Houston, Texas Steven M. Grunberg, MD Department of Hematology/Oncolog...

Patients breathless from chronic lung disease present a serious problem in morbidity and mortality in Britain, the U.S.A., and other countries with a temperate climate (Fletcher and Tinker, 1961 ; Bower, 1961). For their successful treatment it is essential to determine how much obstruction there is to the air-flow from their lungs and to try to find the cause of this obstruction, whether it be...