Thema der Dissertation:
Fast solvers for heterogeneous saddle point problems arising from phasefield-models Thema der Disputation:
Connecting Archimedes and Modern Algorithms: The Computation of Pi
Fast solvers for heterogeneous saddle point problems arising from phasefield-models Thema der Disputation:
Connecting Archimedes and Modern Algorithms: The Computation of Pi
Abstract: The computation of pi, a problem that has fascinated humanity for millennia, is explored in this talk. We trace its evolution from the geometric methods of Archimedes to their adaptation in modern algorithmic approaches.
From a modern perspective, the approximation of a circle's circumference using regular polygons can be understood as a slowly converging algorithm based on the harmonic-geometric mean. This mean is closely related to the arithmetic-geometric mean (AGM), and by exploiting the connection of the AGM to elliptic integrals, a significantly faster-converging algorithm was discovered by Salamin and Brent in the mid-1970s.
We will show that the Brent-Salamin algorithm surprisingly produces iterations identical to those of the second-order algorithm introduced by the Borwein brothers in the mid-1980s, despite being derived from fundamentally distinct theoretical frameworks. Both algorithms are recognized as among the most computationally efficient methods for pi computation and have been employed to set multiple world records in high-precision calculations.
From a modern perspective, the approximation of a circle's circumference using regular polygons can be understood as a slowly converging algorithm based on the harmonic-geometric mean. This mean is closely related to the arithmetic-geometric mean (AGM), and by exploiting the connection of the AGM to elliptic integrals, a significantly faster-converging algorithm was discovered by Salamin and Brent in the mid-1970s.
We will show that the Brent-Salamin algorithm surprisingly produces iterations identical to those of the second-order algorithm introduced by the Borwein brothers in the mid-1980s, despite being derived from fundamentally distinct theoretical frameworks. Both algorithms are recognized as among the most computationally efficient methods for pi computation and have been employed to set multiple world records in high-precision calculations.
Time & Location
Apr 07, 2025 | 01:00 PM
Seminarraum 031
(Fachbereich Mathematik und Informatik, Arnimallee 6, 14195 Berlin)