Skip to main content
SpringerLink
Log in

An algorithm for solving linear algebraic equations using residue arithmetic II

  • Published:
BIT Numerical Mathematics Aims and scope Submit manuscript

Abstract

Part I contained an algorithm for solvingAx=b using single-modulus residue arithmetic. Part II contains a description of the algorithm when more than one modulus is used. There is a discussion of how to select the moduli along with some numerical results. There is a sketch of this procedure in Newman [1]. However, the treatment here is complete and uses the notation of Szabó and Tanaka [2]. It lays the foundation for a subsequent paper which will extend these results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Newman, M.,Solving Equations Exactly, Jour. Res. N.B.S., v. 17B (1967), pp. 171–179.

    Google Scholar 

  2. Szabó, S., and R. Tanaka,Residue Arithmetic and Its Applications to Computer Technology, New York, McGraw Hill, 1967.

    Google Scholar 

  3. Howell, J. A., and R. T. Gregory,Solving Systems of Linear Algebraic Equations Using Residue Arithmetic, University of Texas Computation Center Report TNN-82 (revised), Austin, 1969.

  4. Borosh, I., and A. S. Fraenkel,Exact Solutions of Linear Equations with Rational Coefficients by Congruence Techniques, Math. of Comp. 20 (1966), pp. 107–112.

    Google Scholar 

  5. Todd, John,Survey of Numerical Analysis, New York, McGraw-Hill, 1962, p. 242.

    Google Scholar 

  6. Lietzke, M. H., R. W. Stoughton, and Marjorie P. Lietzke,A Comparison of Several Methods for Inverting Large Symmetric Positive Matrices, Math. of Comp. 18 (1964), pp. 449–456.

    Google Scholar 

  7. Gregory, R. T., and D. L. Karney,A Collection of Matrices for Testing Computational Algorithms, New York, Wiley, 1969.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computation Center, University of Texas, Austin, Dexas, USA

    Jo Ann Howell & Robert T. Gregory

Authors
  1. Jo Ann Howell
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Robert T. Gregory
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Howell, J.A., Gregory, R.T. An algorithm for solving linear algebraic equations using residue arithmetic II. BIT 9, 324–337 (1969). https://doi.org/10.1007/BF01935864

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01935864

Keywords

Search

Navigation