Newton-Raphson reciprocal approximation , 1/x and 1/sqrt(x)

Version 1.0.1 (20.2 KB) by Gert Kruger
The Newton-Raphson approximation of the reciprocal, i.e. 1/x and square root reciprocal is provided along with accuracy testing jigs.
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Updated Wed, 29 May 2019 15:51:19 +0000

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The reciprocal calculation in a real-time controller is quite computationally expensive. The Newton-Raphson approximation of the reciprocal saves on the computational cost at the expense of accuracy. If the reciprocal of an input signal is calculated, with the signal itself having a limited change from one execution cycle to the next, then the previously calculated Newton-Raphson reciprocal serves as an initial "guess" to the new the iteration. This results in a large improvement in accuracy.

The number of iterations can be modified according to the required accuracy.

An analysis can be found in:
Fowler, D. L., and James E. Smith. "An accurate, high speed implementation of division by reciprocal approximation." Proceedings of 9th Symposium on Computer Arithmetic. IEEE, 1989.

Cite As

Gert Kruger (2024). Newton-Raphson reciprocal approximation , 1/x and 1/sqrt(x) (https://www.mathworks.com/matlabcentral/fileexchange/71675-newton-raphson-reciprocal-approximation-1-x-and-1-sqrt-x), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2010a
Compatible with any release
Platform Compatibility
Windows macOS Linux

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Version Published Release Notes
1.0.1

Removed an unnecessary variable from the reciprocal calculation which was used for performance analysis. The functions are now suitable for use (copy and paste).

1.0.0