................................................................................................................................... i ACKNOWLEDGMENTS ............................................................................................................ ii LIST OF FIGURES ...................................................................................................................... ...

A general formula is developed which gives the "best" approximation for any linear functional on the Hardy space H1. Some "best" approximations are given for interpolation, differentiation, and integration and are compared to polynomial approximations.

Many simulation algorithms (chemical reaction systems, differential systems arising from the modeling of transient behavior in the process industries and etc.) contain the numerical solution of systems of differential equations. For the efficient solution of the above mentioned problems, linear multistep methods or Runge-Kutta technique are used. For the simulation of chemical procedures the ra...