On Computing General Root Algorithms Based on Binomial Expansion, Bernoulli’s Method of Continuous Compound Interest, Series Expansion and Other Modification Methods

Author(s)	K. Dikomang, R. Tshelametse, T. Yane
Country	Botswana
Abstract	Most of the Pth root algorithms exhibit high latency or small convergence rates when iteratively computing the roots. Here we present a slew of algorithms based on series expansions of binomial form, and exponential terms that show low latency or small computational cost for finding the Pth root. The latency decreases if the family of series taken are truncated at higher terms. We show that Babylonian method converges quadratically while the binomial series show an increase in convergence rate from quadratic, cubic and higher order O(t^N) convergence rate as the series is sequentially truncated at higher order terms.
Keywords	binomial expansion, Newton Rhapson method, Babylonian method, computational cost.
Field	Mathematics
Published In	Volume 6, Issue 1, January-February 2024
Published On	2024-02-29
Cite This	On Computing General Root Algorithms Based on Binomial Expansion, Bernoulli’s Method of Continuous Compound Interest, Series Expansion and Other Modification Methods - K. Dikomang, R. Tshelametse, T. Yane - IJFMR Volume 6, Issue 1, January-February 2024. DOI 10.36948/ijfmr.2024.v06i01.10717
DOI	https://doi.org/10.36948/ijfmr.2024.v06i01.10717
Short DOI	https://doi.org/gtktkf

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