Erik Jacobsen I live here

Hasselager, Denmark

Hasselager, Denmark

- Erik Jacobsen:
Unification and anti-unification, June 1991 (230kB pdf)

Unification as defined by Robinson [Rob65] is one of two dual concepts, the other is called anti-unification. These concepts are presented in terms of category theory and concepts from algebra.

The unification algorithm from [Rob65] is presented and I argue that it has a worst-case exponential runtime. Modifying this algorithm, I remove one source of exponential runtime. Paterson & Wegman showed in [PW78] that a linear unification algorithm exists. I present this algorithm and compare actual runtimes for all algorithms.

I then present an algorithm for anti-unification by Plotkin [Plo69] and Reynolds [Rey69]. This algorithm has O(n^{2}) runtime. Two new linear algorithms, based on the same principle as the linear Paterson & Wegman unification algorithm, are presented. Finally a parallel anti-unification algorithm from [KMPP88] is presented. - Erik Jacobsen:
The Optimal Linear Least Squares Problem and Methods of Nonlinear Optimization with
Constraints, December 1992 (375kB pdf)

This report investigates various ways of doing nonlinear optimization with constraints. Methods used include the penalty method, the simplex method, pattern search, Newton-Raphson, and Hestenes-Powell.

Testing each method an optimal linear least squares problem is used. Programs in Pascal are provided. In addition parts of the mathematics involved is presented.

I live in Denmark. I write programs for websites and computers. 1 wife, 2 kids, no rabbit, 3 cats.

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