Some observations on algorithms of the Gauss-Borchardt type
Some observations on algorithms of the Gauss-Borchardt type
A one parameter family of algorithms is studied, which contains both the arithmetic-geometric mean of Gauss and its generalization by Borchardt, recently studied by J. and P. Borwein. We prove that the presence of an asymptotic formula for such an algorithm is, in view of the Poisson summation formula, equivalent …