Interval methods and software have been developed over the years for a wide range of problems in scientific computing. However, in order to be able to apply these methods, which give results of guaranteed accuracy, one needs to find ways to improve the efficiency of the computations. For ill-conditioned problems variable precision interval computation is often effective. The two main approaches investigated in this project involve improving the efficiency of variable precision computing and parallelizing the interval algorithms for speed-up using distributed networks of computers. Preliminary studies indicate the possibility of very significant speed-up times when the methods can be parallelized for a network of computers. The investigator has obtained some results for a problem from chemical engineering and for a problem involving the onset of turbulence in wind shears. As algorithmic progress is made, it will become possible to solve other important real world problems with guaranteed accuracy. Such guarantees are crucial in many engineering problems involving safety and environmental issues.
