Advertisement

Exact solution of computational problems via parallel truncated p-adic Arithmetic

  • C. Limongelli
Part of the Texts and Monographs in Symbolic Computation book series (TEXTSMONOGR)

Abstract

The aim of the paper is to show the effectiveness of the p-adic arithmetic in scientific computation by selecting and solving problems which manipulates “big” numbers.

Keywords

Rational Number Parallel Algorithm Computational Problem Code Length Sequential Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aho, A. V., Hopcroft, J. E., Ullman, J. D. (1975): The design and analysis of computer algorithms. Addison Wesley, Reading, MA.Google Scholar
  2. Buchberger, B. (1965): Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal. Ph.D. thesis, University of Innsbruck, Innsbruck, Austria.Google Scholar
  3. Buchberger, B., Loos, R. (1983): Algebraic simplification. In: Buchberger, B., Collins, G. E., Loos, R. (eds.): Computer algebra, symbolic and algebraic computation, 2nd edn. Springer, Wien New York, pp. 11–43.Google Scholar
  4. Buchberger, B., Collins, G. E., Encarnacion, M., Mandache, A. (1993): A SACLIB 1.1 user’s guide. Tech. Rep. 93–19, RISC Linz, Johannes Kepler University, Linz.Google Scholar
  5. Buhr, A., Stroobosscher, R. A. (1990): Providing light-weight concurrency on sharedmemory multiprocessors computers running unix. Software Pract. Exper. 20: 929–964.CrossRefGoogle Scholar
  6. Colagrossi, A., Limongelli, C. (1988): Big numbers p-adic arithmetic: a parallel approach. In: Mora, T. (ed.): Applied algebra, algebraic algorithms and error-correcting codes. Springer, Berlin Heidelberg New York Tokyo, pp. 169–180 (Lecture notes in computer science, vol. 357).Google Scholar
  7. Colagrossi, A., Limongelli, C., Miola, A. (1997): p-adic arithmetic as a tool to deal with power series. In: Miola, A., Temperini, M. (eds.): Advances in the design of symbolic computation systems. Springer, Wien New York, pp. 53–67 (this volume).CrossRefGoogle Scholar
  8. Collins, G. E. (1975): Quantifier elimination for real closed fields by cylindrical algebraic decomposition. In: Brakhage, H. (ed.): Automata theory and formal languages. Springer, Berlin Heidelberg New York, pp. 134–183 (Lecture notes in computer science, vol. 33).Google Scholar
  9. Collins, G. E., Encarnacion, M., Mandache, A., Buchberger, B. (1993): SACLIB user’s guide. RISC Linz, Johannes Kepler University, Linz.Google Scholar
  10. Dittenberger, K. (1987): An efficient method for exact numerical computation. Diploma thesis, Johannes Kepler University, Linz, Austria.Google Scholar
  11. Gregory, R., Krishnamurthy, E. (1984): Methods and applications of error-free computation. Springer, New York Berlin Heidelberg.CrossRefMATHGoogle Scholar
  12. Jebelean, T. (1993): Improving the multiprecision euclidean algorithm. In: Miola, A. (ed.): Design and implementation of symbolic computation systems. Springer, Berlin Heidelberg New York Tokyo, pp. 45–58 (Lecture notes in computer science, vol. 722).CrossRefGoogle Scholar
  13. Knuth, D. E. (1981): The art of computer programming, vol. 2, seminumerical algorithms. 2nd edn. Addison-Wesley, Reading, MA.MATHGoogle Scholar
  14. Koblitz, N. (1977): p-adic numbers, p-adic analysis and Zeta functions. Springer, New York Berlin Heidelberg.CrossRefGoogle Scholar
  15. Krishnamurthy, E. V. (1985): Error-free polynomial matrix computations. Springer, New York Berlin Heidelberg.CrossRefMATHGoogle Scholar
  16. Limongelli, C. (1987): Aritmetiche non-standard: implementazione e confronti. Laurea thesis, University of Rome “La Sapienza”, Rome, Italy.Google Scholar
  17. Limongelli, C. (1993): On an efficient algorithm for big rational number computations by parallel p-adics. J. Symb. Comput. 15: 181–197.MathSciNetCrossRefMATHGoogle Scholar
  18. Loidl, H. W. (1993): A parallel Chinese remainder algorithm on a shared memory multiprocessors. Tech. Rep. 93–09, RISC Linz, Johannes Kepler University, Linz.Google Scholar
  19. Wang, D. (1991): On the parallelization of characteristic-set-based algorithms. Tech. Rep. 91–30, RISC Linz, Johannes Kepler University, Linz.Google Scholar

Copyright information

© Springer-Verlag Wien 1997

Authors and Affiliations

  • C. Limongelli

There are no affiliations available

Personalised recommendations