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The Iterative Solution of General Finite Linear Systems VIA Flexible New Dual Variational Principles
| Speaker | Dr. Elmor L. Peterson |
|---|---|
| Organization | Army Research Office and Systems Science Consulting, Research Triangle, North Carolina |
| Location | EBII Room 1230 |
| Start Date | November 9, 2007 12:30 PM |
| End Date | November 9, 2007 1:30 PM |
These dual variational principles, which come directly from the conjugate duality of generalized by linearly constrained geometic programming, provide promising new theoretical approaches to numerically solving general systems of linear equations and/or linear inequalities – including general linear optimization problems. The resulting solution methodologies require only the numerical computation of a critical solution for an unconstrained objective function – carefully chosen for each individual problem from an infinite number of candidate functions, with the intent of possible exploiting any special system structure (such as sparsity). This infinite flexibility might make these new iterative solution methodologies competitive with the previously developed iterative solution methodologies for solving large-scale linear systems – including both the conjugate-gradient method for symmetric positive-definite systems of linear equations and the interior-point methodologies for linear optimization. In any even, these new dual variational principles also provide a framework for possible generalizing the Moore-Penrose generalized inverse to general finite linear systems. Finally, this paper provides an introduction to the basic ideas and fundamental theory of generalized geometric programming within the familiar context of elementary linear algebra, using only advanced calculus and elementary convexity theory.
SPEAKER BIOGRAPHY
Professor Peterson received a BS degree in physics, as well as MS and PhD degrees in mathematics – all from Carnegie-Mellon University. A co-author of the 1967 book “geometric programming”, which was translated into Russian in 1972 and which spawned the publication of at least four books as well as numerous other publications, he is also the author or co-author of approximately fifty research papers, including ten by invitation. Originally at Westinghouse Research & Development Center, he has also been on the faculties at the University of Michigan [Ann Arbor], Northwestern University and NC State University [Raleigh], as well as a visitor at Stanford University, the US Army Mathematics Research Center at the University of Wisconsin [Madison], and West Virginia University. Having given approximately eight invite lectures at national or international conferences and major research centers, he has also guided the research of fifteen PhD students, at least two of whom have endowed chairs at major research universities, with at least one being a dean. Having served as a consultant for seven organizations, Peterson is currently serving as an interim Program Manager for the Army Research Office.
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