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.

This paper examines the performance of time of arrival (TOA) estimation techniques for an UWB system employing a non-coherent energy collection receiver. The performance of two different algorithms, namely, the threshold-crossing (TC) and the maximum selection (MAX) algorithms, are compared in terms of TOA estimation error. The effect of the TOA estimation error on position calculation is evalu...

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 (...

This paper explores the convergence of nonlinear conjugate gradient methods without restarts, and with practical line searches. The analysis covers two classes of methods that are globally convergent on smooth, nonconvex functions. Some properties of the Fletcher-Reeves method play an important role in the first family, whereas the second family shares an important property with the Polak-Ribir...

Conjugate gradient methods are efficient for smooth optimization problems, while there are rare conjugate gradient based methods for solving a possibly nondifferentiable convex minimization problem. In this paper by making full use of inherent properties of Moreau-Yosida regularization and descent property of modified conjugate gradient method we propose a modified Fletcher-Reeves-type method f...

Epileptic seizures correspond to episodes of increased rhythmicity of the normally chaotic activity in biological neural networks. We propose to use hybrid neural networks where artificial neural networks are used to control the biological neural networks by learning their different states. The learning is dramatically accelerated when using a conjugate gradient method in conjunction with the F...

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...

We develop and analyze a broad family of stochastic/randomized algorithms for inverting a matrix. We also develop specialized variants maintaining symmetry or positive definiteness of the iterates. All methods in the family converge globally and linearly (i.e., the error decays exponentially), with explicit rates. In special cases, we obtain stochastic block variants of several quasiNewton upda...

The solubility of CO2 in the primary, secondary, tertiary and sterically hindered amine aqueous solutions at various conditions was studied. In the present work, the Modified Kent-Eisenberg (M-KE), the Extended Debye-Hückel (E-DH) and the Pitzer models were employed to study the solubility of CO2 in amine aqueous solutions. Two explicit equations are presented to evalu...