George F. Corliss

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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 each step of the(More)
The numericalmethods employed in the solution of many scienti c computing problems require the computation of derivatives of a function f R R Both the accuracy and the computational requirements of the derivative computation are usually of critical importance for the robustness and speed of the numerical solution ADIFOR Automatic Di erentiation In FORtran(More)
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 survey(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 \small(More)
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 reverse(More)
A new framework for analyzing time series data called Time Series Data Mining (TSDM) is introduced. This framework adapts and innovates data mining concepts to analyzing time series data. In particular, it creates a set of methods that reveal hidden temporal patterns that are characteristic and predictive of time series events. Traditional time series(More)
We describe algorithms for computing the greatest common divisor (GCD) of two univariate polynomials with inexactlyknown coe cients. 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 coe cients of the \best" GCD. We discuss various(More)
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 In(More)
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-Muhanna(More)
While conventional computational differentiation based on the forward or reverse modes allows highly accurate computation of derivatives, there are situations where these modes fail to produce the values of derivatives, although the underlying function is differentiable. Typical examples of this phenomenon are connected to the occurrence of branch points in(More)