Plenary Lecture
On Digit Sum of Very Large Integers – An Algorithm to Expand the Capacity of a Computer for Representing Numerical Values
Professor Yixun Shi
Department of Mathematics, Computer Science and Statistics
Bloomsburg University of Pennsylvania
USA
E-mail: yshi@bloomu.edu
Abstract: Every computer, no matter how advanced it is, has a limited capacity for representing numerical values. Suppose M is the largest integer representable on a computer, then only (part of) integers of log10M +1 digits or less can be represented by that computer. This presentation will propose an algorithm that enables the same computer to conduct various computations based on the digit sum of integers of as many as [M/9] digits. The implementation of this algorithm allows us to use this computer to numerically evaluate and theoretically analyze integers that are beyond the representation capacity of this computer. The algorithm is also very suitable for parallel computing. An application of this algorithm is included. A mathematical conjecture related to this algorithm is also raised.
Brief Biography of the Speaker: Yixun Shi graduated with a B.S. degree in mathematics from Anhui Normal University, China in 1981, and then with a M.S. degree in mathematics from Shanghai Normal University, China in 1984. From 1984 to 1987 he taught in the Department of Mathematics of Shanghai Normal University, China. From 1987 to 1992 He studied in the University of Iowa, USA, and graduated in 1992 with a Ph.D. degree in mathematics. Since then he has been a faculty member of the Department of Mathematics, Computer Science and Statistics at the Bloomsburg University of Pennsylvania, USA, serving as an assistant professor from 1992 to 1996, an associate professor from 1996 to 2000, and a full professor since 2000. His research interests include numerical optimization and nonlinear system of equations, scientific computing, computational statistics, mathematical modeling, financial mathematics, and mathematics education. He is author of a number of books and more than 50 papers published in international journals and conference proceedings. He has also delivered keynote speeches at various international conferences.