Some observations on algorithms of the Gauss-Borchardt type

DOI10.1017/S0013091500005198zbMath0746.39006MaRDI QIDQ3985497

Jaak Peetre

Publication date: 27 June 1992

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

convergencefixed pointsfunctional equationsasymptotic formulasGauss's medium arithmetico-geometrium algorithmreal and complex iterationtruncated Borchardt algorithm

Mathematics Subject Classification ID

Topological dynamics (37B99) Fixed-point theorems (47H10) Functional equations for real functions (39B22) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Iteration theory, iterative and composite equations (39B12) Algorithms for approximation of functions (65D15) Iteration of real functions in one variable (26A18) Functional equations for complex functions (39B32) Elliptic integrals as hypergeometric functions (33C75)

Related Items (1)

On some iterated means arising in homogenization theory.

Cites Work

• Generalizing the arithmetic geometric mean - a hapless computer experiment
• [https://portal.mardi4nfdi.de/wiki/Publication:3829784 On the Mean Iteration (a, b) ← � � a+3b 4 , √ab+b 2 � �]
• A Cubic Counterpart of Jacobi's Identity and the AGM

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