Stephen A. Vavasis
Associate Professor
Ph.D. Stanford University, 1989

As computer hardware becomes more powerful, there is a corresponding growth in the demand for more efficient algorithms to solve large-scale scientific problems. My research is on the design and analysis of such algorithms. One area of interest is algorithms for optimization. With Ph.D. student Patricia Hough, we have developed methods for stably solving the weighted least squares problems arising in interior point methods. This new method has been tested using state-of-the-art software for linear programming and is found to be much more robust in the case of near degenerate. With PhD student Elena Bobrovnikova, we are investigating iterative methods for weighted least squares and considering applications to electrical networks.

With Hough and John Gilbert of Xerox PARC, we are developing a method for efficiently computing the "layered least squares'' step in an interior point method. The layered step, a new search direction introduced by Vavasis and Ye, has the potential to lead to much more efficient solution of linear programming problems.

Work on geometry in scientific computing also continues. An improved version of QMG is scheduled for release in June, 1996. QMG is a three-dimensional volumetric unstructured mesh generator for very general polyhedral regions with guaranteed aspect ratio bound, developed jointly with S. Mitchell of Sandia. In new work with PhD student Tobin Driscoll, we have developed an algorithm for conformal mapping of a polygon. The new algorithm can find the correct conformal map for any polygon even if it is elongated, unlike previous algorithms for the problem. The new algorithm can be used for extremely accurate solutions of Laplace's equation and also for two-dimensional structured mesh generation.


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