This presents a set of test problems for nonlinear equations and nonlinear least-squares algorithms. These problems, sent to us by C.V. Nelson of the Maine Medical Center, come from a dipole model of the heart. They are ...

A very important problem in numerical optimization is to find a way to update a sparse Hessian approximation so that it will be positive definite under reasonable circumstances. This problem has motivated research, which ...

The Computer Science faculty at Rice University proposes to design and implement an experimental distributed computing system to support numerical computation. Although local networks of single user machines have already ...

Many computational fluids problems are described by nonlinear parabolic partial differential equations. These equations generally involve advection (transport) and a small diffusion term, and in some cases, chemical ...

The recent success of vector computers like the Cray-1 and array processors such as those manufactured by Floating Point Systems has increased interest in making vector operations available to the Fortran programmer. The ...

In this research we present a trust region algorithm for solving the equality constrained optimization problem. This algorithm is a variant of the 1984 Celis-Dennis-Tapia algorithm. The augmented Lagrangian function is ...

We introduce an approach to velocity and reflectivity estimation based on optimizing the coherence of multiple shot-gather inversions of reflection seismograms. The resulting algorithm appears to avoid the severe convergence difficulties reported for output (nonlinear) least-squares inversion. We describe in detail an algorithm appropriate for the layered acoustic model, using the convolutional model of the plane-wave (p-tau) seismogram. We give a theoretical analysis and numerical evidence that coherency optimization, as defined here, yields stable and reasonably accurate estimates of both velocity trend and reflectivity, by exploiting reflection phase moveout and amplitudes in a computationally efficient way. We also indicate how the approach may be modified to apply to laterally heterogeneous acoustic models, and (more briefly) to determination of elastic models and source parameters as well....

In this paper we develop a unified theory for establishing the local and q-superlinear convergence of the secant methods from the convex class that take advantage of the structure present in the Hessian in constructing ...