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Date: 4-11-2020
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The Brent-Salamin formula, also called the Gauss-Salamin formula or Salamin formula, is a formula that uses the arithmetic-geometric mean to compute pi. It has quadratic convergence. Let
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and define the initial conditions to be , . Then iterating and gives the arithmetic-geometric mean , and is given by
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King (1924) showed that this formula and the Legendre relation are equivalent and that either may be derived from the other.
REFERENCES:
Borwein, J. M. and Borwein, P. B. Pi & the AGM: A Study in Analytic Number Theory and Computational Complexity. New York: Wiley, pp. 48-51, 1987.
Castellanos, D. "The Ubiquitous Pi. Part II." Math. Mag. 61, 148-163, 1988.
King, L. V. On the Direct Numerical Calculation of Elliptic Functions and Integrals. Cambridge, England: Cambridge University Press, 1924.
Lord, N. J. "Recent Calculations of : The Gauss-Salamin Algorithm." Math. Gaz. 76, 231-242, 1992.
Salamin, E. "Computation of Using Arithmetic-Geometric Mean." Math. Comput. 30, 565-570, 1976.
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كيف تساهم الأطعمة فائقة المعالجة في تفاقم مرض يصيب الأمعاء؟
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مشروع ضخم لإنتاج الهيدروجين الأخضر يواجه تأخيرًا جديدًا
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المجمع العلمي يختتم دورته القرآنية في فن الصوت والنغم بالطريقة المصرية
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