# George F. Corliss

The numerical methods employed in the solution of many scientiic computing problems require the computation of derivatives of a function f : R n ! R m. Both the accuracy and the computationalrequirements of the derivativecomputation are usually of critical importance for the robustness and speed of the numerical solution. ADIFOR (Automatic Diierentiation Inâ€¦ (More)
• 1982
Equations Taylor series methods compute a solution to an initial value problem in ordinary differential equations by expanding each component of the solution in a long series. A portable translator program accepts statements of the system of differential equations and produces a portable FORTRAN object code which is then run to solve the system. At eachâ€¦ (More)
• 10
• In many practical problems in which derivatives are calculated, their basic purpose is to be used in the modeling of a functional dependence, often based on a Taylor expansion to rst or higher orders. While the practical computation of such derivatives is greatly facilitated and in many cases is possible only through the use of forward or reverseâ€¦ (More)
The formal process of the evaluation of derivatives using some of the various modern methods of computational diierentiation can be recognized as an example for the application of conventional \approximate" numerical techniques on a non-archimedean extension of the real numbers. In many cases, the application of \innnitely small" numbers instead of \smallâ€¦ (More)
• 1999
Compared to standard numerical methods for initial value problems (IVPs) for ordinary diierential equations (ODEs), validated methods for IVPs for ODEs have two important advantages: if they return a solution to a problem, then (1) the problem is guaranteed to have a unique solution, and (2) an enclosure of the true solution is produced. The authors surveyâ€¦ (More)
and his brother, who will arrive shortly. iii Acknowledgment I would like to thank Dr. Xin Feng for the encouragement, support, and direction he has provided during the past three years. His insightful suggestions, enthusiastic endorsement, and shrewd proverbs have made the completion of this research possible. They provide an example to emulate. I owe aâ€¦ (More)
• 1998
We describe algorithms for computing the greatest common divisor GCD of two univariate polynomials with inexactly-known coeecients. Assuming that an estimate for the GCD degree is available e.g., using an SVD-based algorithm, we formulate and solve a nonlinear optimization problem in order to determine the coeecients of the best" GCD. We discuss variousâ€¦ (More)
• 2006
The idea of containment sets (csets) is due to Walster and Hansen, and the theory is mainly due to the first author. Now that floating point computation with infinities is widely accepted, it is necessary to achieve the same for interval computation. The cset of a function over a set in its domain space is the set of all limits of normal function valuesâ€¦ (More)
• 1
• 2007
Structural engineers use design codes formulated to consider uncertainty for both reinforced concrete and structural steel design. For a simple one-bay structural steel frame, we survey typical uncertainties and compute an interval solution for displacements and forces. The naive solutions have large over-estimations, so we explore the Mullen-Muhannaâ€¦ (More)
Eliminating malaria requires vector control interventions that dramatically reduce adult mosquito population densities and survival rates. Indoor applications of insecticidal nets and sprays are effective against an important minority of mosquito species that rely heavily upon human blood and habitations for survival. However, complementary approaches areâ€¦ (More)