Scientific Computing

This module demonstrates the BFGS method for minimizing a nonlinear function in two dimensions. Given an approximate solution value, a new approximate solution value is given by the minimum of a local quadratic approximation to the objective function. The step to the new point is given by the solution to a linear system involving an approximation to the Hessian matrix of the objective function, with the negative of its gradient as right-hand side. The process is repeated until convergence, which is usually fairly rapid.

The user selects a problem either by choosing a preset example or
typing in a desired objective function *f*(*x*,
*y*)*x*, *y*)*x*, *y*)*s* is computed by solving a
linear system *B*** s** =
−∇

**Reference:** Michael T. Heath, *Scientific Computing,
An Introductory Survey*, 2nd edition, McGraw-Hill, New York,
2002. See Section 6.5.5, especially Algorithm 6.5 and Example 6.13.

**Developers:** Jeffrey Naisbitt and Michael Heath