Multivariate secant method

Associativity of the Secant Method

1. INTRODUCTION. This paper has its genesis in a problem the author first came upon while in college. Although the areas covered here are well travelled and nothing here is guaranteed original, it covers a pleasant nexus of many mathematical strands. Furthermore, we show the value of good notation and of reading an old master for solving a problem. Consider iterates of the function m (x) = 1 I ...

A secant method for nonsmooth optimization

The notion of a secant for locally Lipschitz continuous functions is introduced and a new algorithm to locally minimize nonsmooth, nonconvex functions based on secants is developed. We demonstrate that the secants can be used to design an algorithm to find descent directions of locally Lipschitz continuous functions. This algorithm is applied to design a minimization method, called a secant met...

Parameter Identification by a Generalised Secant Method

An efficient secant-method based algorithm for solving nonlinear least squares problem is presented which showed good stability and convergence properties even with relatively high number of unknowns and large system response deviations. The trial solutions were generated by a special transformation in each iteration step. The distance between observed and simulated system responses were define...

A modified secant method for unconstrained minimization

Faster Relief Mapping using the Secant Method

Relief mapping using the secant method offers an efficient method for adding per pixel height field based displacement to an arbitrary polygonal mesh in real time. The technique utilizes an interval based method in which bounds of the interval are computed in the beginning and are refined at every iteration until the intersection point is reached. The search space defined by the interval reduce...