Brent’s Method of Finding Roots and Inverse Functions: Algorithms for Grad Students (1)

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Also discusses the Saha Equation, which is fundamental to plasma physics.

Contents
00:00 - Introduction
00:35 - Iterative solutions
01:52 - Root finding
02:59 - Brent method
05:42 - Bounds
07:33 - Python example
08:53 - Saha equation

References
[1] Image of a Casio fx-85GT X Classwiz calculator, (User: L ke)

[2] R. P. Brent, Personal Home Page,
(Accessed 02/08/24)
[3] R. P. Brent, “An algorithm with guaranteed convergence for finding a zero of a function”, The Computer Journal 14, 422 (1971).
[4] R. P. Brent, “Algorithms for Minimisation without Derivatives”, p. 47 (Prentice Hall, 1972).
[5] Scipy Github (Zeros subdirectory), (Accessed 31/07/24)
[6] Experimental double-resonance solid-state Tesla coil II by Dr. Antônio Carlos M. de Queiroz

[7] M. R. Zaghloul, et al., “A simple formulation and solution strategy of the Saha equation for ideal and nonideal plasmas”, J. Phys. D: Appl. Phys. 33, 977 (2000).
[8] Image of a helium filled discharge tube shaped like the element’s atomic symbol (User: Pslawinski)

[9] Green plasma in xenon-nitrogen mixture by Carl Willis,

[10] B. A. Remington et al., “Rayleigh-Taylor instabilities in high-energy density settings on the National Ignition Facility” PNAS 116, 18233 (2019).