On rational approximation and its applications
We are encountering more and more rare event probability problems as we move toward the information age. When systems are large or complex, it takes tremendous computing resources to solve these problems. Typically, it is easy to get simulation results at high probability values and these system functions usually have nice properties.
These opens the door for the application of rational approximation algorithms. Rational approximation has been applied in quite a few performance evaluation problems in communication/computer systems. This dissertation further extends the research in this area. We first used several benchmark problems to verify the effectiveness of rational approximation algorithm. Then rational approximation based algorithms are developed to solve some problems in the networking area, such as the blocking probability analysis of optical networks and the reliability analysis of networks. When dealing with these problems, extensive experiments have been carried out to give convincing results. Our results indicate that rational approximation method is promising for applications in many areas. We also developed a method to estimate the error of rational approximants when there exist errors in the interpolation points.