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Application of Continued Fractions for Fast Evaluation of Certain Functions on a Digital Computer
March 1974 (vol. 23 no. 3)
pp. 301-309
| ASCII Text | x | ||
| A. Bracha-Barak, "Application of Continued Fractions for Fast Evaluation of Certain Functions on a Digital Computer," IEEE Transactions on Computers, vol. 23, no. 3, pp. 301-309, March, 1974. | |||
| BibTex | x | ||
| @article{ 10.1109/T-C.1974.223926, author = {A. Bracha-Barak}, title = {Application of Continued Fractions for Fast Evaluation of Certain Functions on a Digital Computer}, journal ={IEEE Transactions on Computers}, volume = {23}, number = {3}, issn = {0018-9340}, year = {1974}, pages = {301-309}, doi = {http://doi.ieeecomputersociety.org/10.1109/T-C.1974.223926}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Computers TI - Application of Continued Fractions for Fast Evaluation of Certain Functions on a Digital Computer IS - 3 SN - 0018-9340 SP301 EP309 EPD - 301-309 A1 - A. Bracha-Barak, PY - 1974 KW - Bilinear transformation KW - binary arithmetic KW - continued fractions KW - quadratic equation KW - Riccati equation KW - selection rules. VL - 23 JA - IEEE Transactions on Computers ER - | |||
The purpose of this paper is to develop a method for evaluation of certain elementary functions on a digital computer by the use of continued fractions. The time required for this evaluation is drastically reduced by using "short" operations like shift and add, instead of multiplications. Functional consistency is the most important factor that aliows the expansion of a function into a continued fraction. Several cases are discussed; in particular the solution of the quadratic equation is discussed in more detail to demonstrate the convergence of the method.
Index Terms:
Bilinear transformation, binary arithmetic, continued fractions, quadratic equation, Riccati equation, selection rules.
Citation:
A. Bracha-Barak, "Application of Continued Fractions for Fast Evaluation of Certain Functions on a Digital Computer," IEEE Transactions on Computers, vol. 23, no. 3, pp. 301-309, March 1974, doi:10.1109/T-C.1974.223926
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