The steepest descent (SD) method is well-known as the simplest in optimization. In this paper, we propose a new SD search direction for solving system of linear equations Ax = b. We also prove that proposed with exact line satisfies condition and possesses global convergence properties. This motivated by previous work on Zubai’ah-Mustafa-Rivaie-Ismail (ZMRI)[2]. Numerical comparisons classical ...

Surface networks capture the topological relations between passes of a continuous surface, the paths of steepest descent and ascent starting at the passes, and the pits and peaks where the steepest paths end. This paper extends the topology of the network in three ways. Objects at the edge of the surface model are introduced. Horizontal areas may represent passes, pits, or peaks, and therefore ...

In this paper we prove a general result establishing a priori L estimates for solutions of RiemannHilbert Problems (RHP’s) in terms of auxiliary information involving an associated “conjugate” problem (see Conjugation Lemma 1.39 below). We then use the result to obtain uniform estimates for a RHP (see Theorem 1.48) that plays a crucial role in analyzing the long-time behavior of solutions of th...

We apply the method of nonlinear steepest descent to compute the longtime asymptotics of the Camassa–Holm equation for decaying initial data, completing previous results by A. Boutet de Monvel and D. Shepelsky.

but it will be clear immediately to the reader with some experience in the field, that the method extends naturally and easily to the general class of wave equations solvable by the inverse scattering method, such as the KdV, nonlinear Schrödinger (NLS), and Boussinesq equations, etc., and also to "integrable" ordinary differential equations such as the Painlevé transcendents. As described, for...

In this paper, we implement the method of Steepest Descent in single and multilayer feedforward artificial neural networks. In all previous works, all the update weight equations for single or multilayer feedforward artificial neural networks has been calculated by choosing a single activation function for various processing unit in the network. We, at first, calculate the total error function ...

We present a version of the gravitational method for linear programming, based on steepest descent gravitational directions. Finding the direction involves a special small “nearest point problem” that we solve using an efficient geometric approach. The method requires no expensive initialization, and operates only with a small subset of locally active constraints at each step. Redundant constra...

In this work, we consider the GPU implementation of the steepest descent method with Fourier acceleration for Laudau gauge fixing, using CUDA. The performance of the code in a Tesla C2070 GPU is compared with a parallel CPU implementation.

The noisy Burgers equation in one spatial dimension is analyzed by means of the Martin-SiggiaRose technique in functional form. In a canonical formulation the morphology and scaling behavior are accessed by mean of a principle of least action in the asymptotic non-perturbative weak noise limit. The ensuing coupled saddle point field equations for the local slope and noise fields, replacing the ...

This paper extends the full convergence of the steepest descent algorithm with a generalized Armijo search and a proximal regularization to solve quasiconvex minimization problems defined on complete Riemannian manifolds. Previous convergence results are obtained as particular cases of our approach and some examples in non Euclidian spaces are given.