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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


About Utility of the Simplified Grünwald-Letnikov Formula Equivalent Horner Form

Discontinuity, Nonlinearity, and Complexity 4(4) (2015) 487--498 | DOI:10.5890/DNC.2015.11.010

Dariusz W. Brzeziński; Piotr Ostalczyk

Institute of Applied Computer Science, Lodz University of Technology, 18/22 Stefanowskiego St.,90-924 Łodź, Poland

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First we discuss some crucial factors that determine numerical calculations accuracy of the Gr¨unwald-Letnikov formula and its equivalent Horner form. Then we introduce simplified variants of both formulas and the concept of the calculation tail. We analyze the utility of its length for mitigation of a time and a memory shortages influence on the accuracy in realtime microprocessor calculations. Credibility of the conclusions is lent by the comparison of the results obtained on a PC and on a real-time DSP system.


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