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Iterative Refinement in Floating Point

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Published:01 April 1967Publication History
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Abstract

Iterative refinement reduces the roundoff errors in the computed solution to a system of linear equations. Only one step requires higher precision arithmetic. If sufficiently high precision is used, the final result is shown to be very accurate.

References

  1. 1 WILKINSON, J. H. Rounding Errors in Algebraic Processes. Prentice-Hall, Englewood Cliffs, N. J., 1963. Google ScholarGoogle Scholar
  2. 2 KAXHAN, W. Writeups of library tape subroutines LEQU, LEQUN, FLEQU, CLEQU nd DLEQU. Inst. Computer Sci., U. of Toronto, 1965 (various months).Google ScholarGoogle Scholar
  3. 3 MOLER, C. SOLVE, Accurate simultaneous linear equation solver with iterative improvement. SHARE Distribution No. 3194, 1964.Google ScholarGoogle Scholar
  4. 4 MeKEEMAN, W.M. Algorithm 135. Crout with equilibration und iteration. Comm. ACM 5 (1962), 553-555. Google ScholarGoogle Scholar
  5. 5 MARTIN, R. S., PERES, G., AND WILKINSON, J .H . Iterative refinement of the solution of positive definite system of equations. Numer. Math. 8 (1966), 203-216.Google ScholarGoogle Scholar
  6. 6 BOWDLER, H. J., MARTIN, R. S., PETERS, G., AND WILKINSON, J. g . Solution of real nd complex systems of equations. Numer. Math. 8 (1966), 217-234.Google ScholarGoogle Scholar

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  1. Iterative Refinement in Floating Point

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          cover image Journal of the ACM
          Journal of the ACM  Volume 14, Issue 2
          April 1967
          219 pages
          ISSN:0004-5411
          EISSN:1557-735X
          DOI:10.1145/321386
          Issue’s Table of Contents

          Copyright © 1967 ACM

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          Association for Computing Machinery

          New York, NY, United States

          Publication History

          • Published: 1 April 1967
          Published in jacm Volume 14, Issue 2

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