Using Interval Analysis to Bound Numerical Errors in Scientific Computing

摘要: In scientific computing, the approximation of continuous physical phenomena by floating-point numbers gives rise to rounding error. The behaviour errors is difficult predict, and most applications ignore it. For in which accuracy result critical, this not an acceptable choice. Interval analysis alternative conventional computation that offers guaranteed error bounds. Despite advantage, interval methods have rarely been applied high performance computing. part, because additional cost associatedwith performing operations over corresponding operations. Another issue lack example analysis; many users simply do know exists. This thesis develops demonstrates techniques can be feasibly Methods are shown codes may significantly improved on UltraSPARC platform: hand-optimised for vector functions developed around 60% faster than Sun implementation, method multiplication 30% used other implementations. benefits demonstrated through application problem: evaluation electrostatic potentials. Alternative analysed: two new accurate summation proposed proven reduce application. demonstration includes what believed first implementation fast multipole method. explore balance between truncation method, has previously ignored. results suggest affect practically achieved using also provide guidance choosing parameters minimise