The truncated basis of adaptively refined multilevel spline spaces was introduced by Giannelli et al. (2012, 2013). It possesses a number of advantages, including the partition of unity property, decreased support of the basis functions, preservation of coefficients and strong stability, that may make it highly useful for geometric modeling and numerical simulation. We generalize this construct...

We extend the scope of analysis for linesearch optimization algorithms on (possibly infinitedimensional) Riemannian manifolds to the convergence analysis of the BFGS quasi-Newton scheme and the Fletcher–Reeves conjugate gradient iteration. Numerical implementations for exemplary problems in shape spaces show the practical applicability of these methods.

More than three decades after the Supreme Court ruling in Regents of the University of California v. Bakke, the diversity rationale for affirmative action in public education remains a topic of political and legal controversy. Many colleges and universities have implemented affirmative action policies not only to remedy past discrimination, but also to achieve a racially and ethnically diverse ...

In order to construct a C1-quadratic spline over an arbitrary triangulation, one can split each triangle into 12 subtriangles, resulting in a finer triangulation known as the Powell-Sabin 12-split. It has been shown previously that the corresponding spline surface can be plotted quickly by means of a Hermite subdivision scheme [5]. In this paper we introduce a nodal macroelement on the 12-split...

We are concerned in this paper with the general problem of finding an unrestricted local minimum of a function J[xu x2 • • •, xn) of several variables xx, x2, • •., xn. We suppose that the function of interest can be calculated at all points. It is convenient to group functions into two main classes according to whether the gradient vector g, = Wbx, is defined analytically at each point or must...

This paper presents a method to control the sway of a rotary crane by using a linear transfer transformation (LTT) model. The LTT model is built and its parameters are geometrically derived. Optimal control of a rotary crane is presented using an optimization method of Fletcher-Reeves so that the load has no sway at the end point of the transfer. The effectiveness of the proposed control method...

Transportation Research Record: Journal of the Transportation Research Board, No. 2311, Transportation Research Board of the National Academies, Washington, D.C., 2012, pp. 186–194. DOI: 10.3141/2311-18 Department of Civil and Environmental Engineering, Portland State University, P.O. Box 751, Portland, OR 97207. Corresponding author: E. Albright, [email protected]. of buses over passenger vehicles (...

In this paper we perform an analysis of the wave structure of the ideal magnetohydrodynamic (MHD) equations. We present an analytical expression of the nonlinearity term associated to each characteristic field derived from a scaled version of the complete system of eigenvectors proposed by Brio andWu [M. Brio, C.C. Wu, An upwind differencing scheme for the equations of ideal magnetohydrodynamic...

Using a Davidon-Fletcher-Powell nonlinear function minimization algorithm," the function 7) is fit to the observed control pressure-volume relationships. The output of this computer subprogram is a set of estimates of the three parameters a,, a2, and a,. Using these parameters in 7), the analysis program computes the predicted pressure at each actually observed cubed circumference, using the mi...

Abstract In this paper, we study and prove the non-asymptotic superlinear convergence rate of Broyden class quasi-Newton algorithms which includes Davidon–Fletcher–Powell (DFP) method Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. The asymptotic these methods has been extensively studied in literature, but their explicit finite–time local is not fully investigated. provide a (non-asymptotic) a...