The Powell singular function was introduced 1962 by M.J.D. Powell as an unconstrained optimization problem. The function is also used as nonlinear least squares problem and system of nonlinear equations. The function is a classic test function included in collections of test problems in optimization as well as an example problem in text books. In the global optimization literature the function ...

A combination of emetine hydrochloride with chloroquine yields better results than either drug alone in the treatment of amoebic liver abscess in adults (Wilmot, Powell, and Adams, 1959). A similar combination of dehydroemetine with chloroquine is equally satisfactory (Wilmot, Powell, MacLeod, and Elsdon-Dew, 1964; Powell, Wilmot, MacLeod, and Elsdon-Dew, 1967). Dehydroemetine is claimed to be ...

Recently we developed multiscale spaces of C piecewise quadratic polynomials relative to arbitrary polygonal domains Ω ⊂ R. These multiscale bases are weakly stable with respect to the L2 norm. In this paper we show that these bases form strongly stable Riesz bases for the Sobolev spaces Hs(Ω) with s ∈ (2, 5 2 ).

We consider the problem of constructing a C1 piecewise quadratic interpolant, Q, to positional and gradient data defined at the vertices of a tessellation of n-simplices in IR. The key to the interpolation scheme is to appropriately subdivide each simplex to ensure that certain necessary geometric constraints are satisfied by the subdivision points. We establish these constraints using the Bern...