Basic linear algebra operations in SLI arithmetic
Symmetric level-index arithmetic was introduced to overcome recognized limitations of floating-point systems, most notably overflow and underflow. The original recursive algorithms for arithmetic operations are parallelizable to some extent, particularly when applied to extended sums or products. The main purpose of this paper is to present parallel SLI algorithms for arithmetic and basic linear algebra operations.
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- 1.M. A. Anuta, D. W. Lozier, N. Schabanel, and P. R. Turner, Basic linear algebra operations in SLI arithmetic, Nat. Inst. Stand. and Tech. Report NISTIR 5811, March 1996, 15 pages.Google Scholar
- 2.M. A. Anuta, D. W. Lozier, and P. R. Turner, The MasPar MP-1 as a computer arithmetic laboratory, J. Res. Nat. Inst. Stand. and Tech. 101 (1996), 165–174.Google Scholar
- 6.C. W. Clenshaw, F. W. J. Olver, and P. R. Turner, Level-index arithmetic: An introductory survey, Numerical Analysis and Parallel Processing (P. R. Turner, ed.), Springer-Verlag, 1989, pp. 95–168.Google Scholar
- 7.C. W. Clenshaw and P. R. Turner, The symmetric level-index system, IMA J. Numer. Anal. 8 (1988), 517–526.Google Scholar
- 8.G. H. Golub and C. F. van Loan, Matrix Computations, 2nd ed., Johns Hopkins University Press, Baltimore, MD, 1989.Google Scholar
- 11.-, Error-bounding in level-index computer arithmetic, Numerical Methods and Error Bounds (G. Alefeld and J. Herzberger, eds.), Akademie Verlag, Berlin, 1996, pp. 138–145.Google Scholar
- 12.N. Schabanel and P. R. Turner, Parallelization and parallel implementation on the MasPar of SLI arithmetic, Mathematics Department, U. S. Naval Academy, Annapolis, MD 21402, September 13, 1995.Google Scholar
- 13.P. R. Turner, A software implementation of SLI arithmetic, Proc. ARITH9, IEEE Computer Society Press, Washington, DC, 1989, pp. 18–24.Google Scholar
- 14.-, Implementation and analysis of extended SLI operations, Proc. ARITH10, IEEE Computer Society Press, Washington, DC, 1991, pp. 118–126.Google Scholar