| An algorithm is proposed for training the single-layered per-ceptron. The algorithm follows successive steepest descent directions with respect to the perceptron cost function, taking care not to increase the number of misclassiied patterns. The problem of nding these directions is stated as a quadratic programming task, to which a fast and eeective solution is proposed. The resulting algorit...

A new method is given for eeecting numerical diierentiation by means of an optimization procedure. The method is shown to be eeective for the diierentiation of noisy functions, and stability and convergence results for a steepest descent implementation are proved.

We extend the Blahut-Arimoto algorithm to continuous memoryless channels by means of sequential Monte Carlo integration in conjunction with steepest descent. As an illustration, we consider the peak power constrained AWGN channel.

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.

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...

Orthogonal greedy learning (OGL) is a stepwise learning scheme that adds a new atom from a dictionary via the steepest gradient descent and build the estimator via orthogonal projecting the target function to the space spanned by the selected atoms in each greedy step. Here, “greed” means choosing a new atom according to the steepest gradient descent principle. OGL then avoids the overfitting/u...

A new Actuator State Based Adaptive (ASBA) motion drive algorithm was developed. In contrast to classical motion drive algorithms a subset of the motion drive parameters are time varying. The ASBA algorithm uses the steepest descent algorithm to adapt these parameters to minimize a pre-defined cost function. The cost function contains penalties on motion cue errors, simulator motion, and the di...

We design and study an adaptive algorithm for the numerical solution of the stationary nonlinear Stokes problem. The algorithm can be interpreted as a disturbed steepest descent method, which generalizes Uzawa’s method to the nonlinear case. The outer iteration for the pressure is a descent method with fixed step-size. The inner iteration for the velocity consists of an approximate solution of ...

3 Reaction-diffusion systems 3 3.0.1 Qualitative analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.1 Exact mathematical result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.2 Representation in phase space: viscosity solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.2.1 Viscosity solution by ste...