The integration to steady state of many initial value ODEs and PDEs using the forward Euler method can alternatively be considered as gradient descent for an associated minimization problem. Greedy algorithms such as steepest descent for determining the step size are as slow to reach steady state as is forward Euler integration with the best uniform step size. But other, much faster methods usi...

AdaBoost is a popular and eeective leveraging procedure for improving the hypotheses generated by weak learning algorithms. AdaBoost and many other leveraging algorithms can be viewed as performing a constrained gradient descent over a potential function. At each iteration the distribution over the sample given to the weak learner is the direction of steepest descent. We introduce a new leverag...

Active control methods have been applied to a number of practical problems in which it is necessary to control a tonal disturbance. For example, the control of engine noise and vibration in vehicles, propeller noise in aircraft and the vibration produced by reciprocating machinery in many industrial systems. In such applications the steepest-descent algorithm has been widely employed, in part d...

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.