- Title
- More quadratically converging algorithms for π
- Creator
- Borwein, J. M.; Borwein, P. B.
- Relation
- Mathematics of Computation Vol. 46, Issue 173, p. 247-253
- Publisher Link
- http://dx.doi.org/10.1090/S0025-5718-1986-0815846-6
- Publisher
- American Mathematical Society
- Resource Type
- journal article
- Date
- 1986
- Description
- We present a quadratically converging algorithm for π based on a formula of Legendre's for complete elliptic integrals of modulus sin(π/12) and the arithmetic-geometric mean iteration of Gauss and Legendre. Precise asymptotics are provided which show this algorithm to be (marginally) the most efficient developed to date. As such it provides a natural computational check for the recent large-scale calculations of π.
- Subject
- pi; arithmetic geometric mean iteration; high precision calculation; quadratically converging algorithms
- Identifier
- http://hdl.handle.net/1959.13/1043612
- Identifier
- uon:14224
- Identifier
- ISSN:0025-5718
- Language
- eng
- Full Text
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| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | ATTACHMENT01 | Publisher version (open access) | 468 KB | Adobe Acrobat PDF | View Details Download |