No abstract

Much of the testing of optimization software is inadequate because the number of test functmns is small or the starting points are close to the solution. In addition, there has been too much emphasm on measurmg the efficmncy of the software and not enough on testing reliability and robustness. To address this need, we have produced a relatwely large but easy-to-use collection of test functions and designed gmdelines for testing the reliability and robustness of unconstrained optimization software.

No abstract

In many nonlinear problems it is necessary to estimate the Jacobian matrix of a nonlinear mapping F. In large-scale problems the Jacobian of F is usually sparse, and then estimation by differences is attractive because the number of differences can be small compared with the dimension of the problem. For example, if the Jacobian matrix is banded, then the number of differences needed to estimate the Jacobian matrix is, at most, the width of the band. In this paper we describe a set of subroutines whose purpose is to estimate the Jacobian matrix of a mapping F with the least possible number of function evaluations.

A software package based on a modification of the Weeks' method is presented for calculating function values f ( t ) of the inverse Laplace transform. This method requires transform values F ( z ) at arbitrary points in the complex plane, and is suitable when f ( t ) has continuous derivatives of all orders; it is especially attractive when f ( t ) is required at a number of different abscissas t .