Taylor expansion of the accumulated rounding error
- Seppo Linnainmaa
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The article describes analytic and algorithmic methods for determining the coefficients of the Taylor expansion of an accumulated rounding error with respect to the local rounding errors, and hence determining the influence of the local errors on the accumulated error. Second and higher order coefficients are also discussed, and some possible methods of reducing the extensive storage requirements are analyzed.
- P. Henrici,Elements of numerical analysis, Ch. 16, Wiley, New York, 1964.
- S. Linnainmaa,The representation of the cumulative rounding error of an algorithm as a Taylor expansion of the local rounding errors, (In Finnish), Master's Thesis, Department of Computer Science, University of Helsinki, Helsinki, Finland, 1970.
- S. Linnainmaa,Towards accurate statistical estimation of rounding errors in floating-point computations, BIT 15 (1975), 165–173.
- S. Linnainmaa,A set of ALGOL procedures for analyzing the behavior of rounding errors in floating-point computations, Report A-1975-2, Department of Computer Science, University of Helsinki, Helsinki, Finland.
- M. Tienari,A statistical model of roundoff errors for varying length floating-point arithmetic, BIT 10 (1970), 355–365.
- M. Tienari,On some topological properties of numerical algorithms, BIT 12 (1972), 409–433.
- Taylor expansion of the accumulated rounding error
BIT Numerical Mathematics
Volume 16, Issue 2 , pp 146-160
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- Kluwer Academic Publishers
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- Seppo Linnainmaa (1)
- Author Affiliations
- 1. Department of Computer Science, University of Helsinki, Töölönkatu 11, SF-00100, Helsinki 10, Finland