Biography
I was born in Leeuwarden in the Netherlands in 1949 and studied Mathematical Engineering at Delft University. I also taught a Numerical Analysis Lab and Matrix Algebra for three years. I spent the last year of my studies as a junior engineer at the Delft Hydraulics Lab in Delft. From 1976 through 1980 I was employed at Twente University in the Mechanical Engineering department where I obtained a doctorate in The Sciences. I emigrated to Canada in 1980 and have spent most of my working years as a scientific programmer in the Oil and Gas industry in Calgary, Alberta. Since 1990, I have worked as a consultant on specialized programming assignments requiring a high degree of mathematical expertise.

Mathematics
The mathematical results I have collected on this website are the result of about 20 years of investigations which I have pursued as a hobby in my spare time. Publishing this material on my own web site allows me to circumvent the time consuming and increasingly political process of submitting to scientific journals. It also allows me to publish some incomplete work essentially as laboratory journals. The material I am publishing here may be incomplete or even incorrect in some way, yet presents valuable ideas and inventions.

Constrained Geodesic
In 1988, I constructed the constrained geodesic, the curve of shortest arclength subject to a set of algebraic equality constraints. From the constrained geodesic I constructed some geometric properties of the manifold defined by the constraints, chiefly its Gauss curvature. Much later, I generalized the result to systems with a combination of holonomic and non-holonomic constraints. It is natural that practical methods for constrained optimization should be derived from the constrained geodesic. I have done some preliminary work on a practical implementation but have not been completely successful. I also discovered that some of the usual results for a surface in three dimensions as treated in classical differential geometry can alternatively be obtained by regarding the surface as a single constraint.

Normalized Hermite Polynomials
I constructed these polynomials to solve the problem of bracketed root finding using higher order interpolation. The new root finding method is based on inverse interpolation using Hermite polynomials which are normalized to a standard interval. The simple reduction to a basis interval implies that the interpolation polynomials can be hard-coded. I have named the resulting root finding method Normalized Inverse Hermite Interpolation (NIH). I present some experimental results using a few common problems and the results indicate that this method is considerably faster than Brent's method for the cases considered.

Functional Approximation
Normalized Hermite Polynomials can also be used to construct methods for the approximation of transcendental functions. Here too, the simple innovation consists of mapping the intervals used in the interval reduction to a single unit interval where hard-coded polynomials can be used for the interpolation. I have some interesting results here but there still is a lot of theory waiting to be discovered. The resulting methods are not necessarily faster but their development is very systematic. There is a potential for research in the field of complex function theory here.

Equilibrium Configurations of Points on the Sphere
In the late 80's my friend Gary G. Ford interested me in this problem and I wrote the first implementation of a program for the computation of stationary and equilibrium configurations. I have used this program and its subsequent incarnations as a vehicle to develop and test methods from Linear Algebra. I developed a bootstrapping algorithm for the systematic search for optima and have used it to assemble a library of optimal solutions for the Maximum Distance objective.

Engineering
I have considerable expertise developing numerical simulation models and have written various simulation models for pipeline networks (liquid and gas) both stationary and transient. I developed a model for the liquid pipeline network of Peace Pipeline (now Pembina Petroleum) in Alberta. The gas surface network model I wrote for PHH Petroleum Consultants has been extremely successful. One of my best achievements has been the design with dr. Krystyna Jungowski of a model for optimization of the Nova natural gas pipeline network. This network is now owned by TransCanada PipeLines and it is one of the most complex in the world counting over 4000 network elements. The Network Optimizer uses a novel algorithm for nonlinear constrained optimization which constructs a Linear Programming model from combinations of the sensitivity vectors of all unknowns in the system with respect to all the free parameters. Most recently I worked at SkyTrac Systems in British Columbia where I developed FlightMap, a Windows program which displays the flight tracks of aircraft on a world map which can be scrolled and zoomed. Finally, I am the author of Exbos, a model for numerical reservoir simulation which is available commercially.

Scientific Programming
I am developing a suite of modules for Numerical Linear Algebra (Matrix Algebra) in the C language with Assembler support. The main objective of this effort is to make available in standard C the best possible algorithms in an implementation which is both eminently readable and maintainable.