PDFAbstract: We describe the use of Newton’s method to compute a high precision approximation to e. This work provides a brief introduction to the the history of computing elementary transcendental functions and numbers, presents a novel method for computing e, examines the quadratic convergence of Newton’s method in this application, and makes use of multi-precision arithmetic available in Python to compute e to any desired precision.
Keywords: computing Euler’s number, Newton’s method, quadratic convergence
Cite this paper
Emerson Miller, Douglas Salane. (2024) A Quadratically Convergent Method for Computing Euler’s Number. International Journal of Mathematical and Computational Methods, 9 , 105-108
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