EVENTS

TODAY

CARMA Summer Student and RHD Seminar

"Backtest overfitting demonstration tool"
Dr Amir Salehipour

Location: V205 Mathematics Building
Date: 12:00 pm, Thu, 29th Jan 2015

TOMORROW

Discipline Meeting

Location: TBA
Date: 9:00 am, Fri, 30th Jan 2015

Time to be advised

Summer Scholar Presentations

Location: V206 Mathematics Building
Date: 12:00 pm, Tue, 3rd Feb 2015

Summer student presentations, details to follow.

SPCOM 2015: South Pacific Continuous Optimization Meeting

Location: Adelaide (University of South Australia)
Date: 9:00 am, Sun, 8th Feb 2015

SPCOM 2015 will offer a rich scientific program consisting of Conference Talks, a Fitzpatrick Workshop, two half-day Tutorials, and a Poster Session. Further details and a list of speakers are available on the conference website.

These are the events in the next 7 days. For more, see the events page.

CONFERENCES

Coming up next: SPCOM (in Adelaide)! (8-12 February)

NEWS

Congratulations to Cameron Rogers

Cameron received an Honourable Mention for his talk "Using Random walks to estimate the shape of Folner Sets" at the 8th Australia and New Zealand Mathematics Convention in Melbourne last week.

More promotion: PROF Ljiljana Brankovic

CARMA member Ljiljana Brankovic has been promoted to full professor. Congratulations!

Matt Tam awarded CTAC prize for talk

CARMA PhD student Matthew Tam has been awarded one of four student prizes for his talk "Reflection Methods for Inverse Problems" at the biennial Computation Techniques and Applications ... [READ MORE]

HIGHLIGHTS

Selected paper from DocServer
Jonathan M. Borwein, Richard E. Crandall, Greg Fee

ABSTRACT

The Ramanujan AGM fraction is a construct $${\cal R}_\eta(a,b) =\,\frac{a}{\displaystyle \eta+\frac{b^2}{\displaystyle \eta +\frac{4a^2}{\displaystyle \eta+\frac{9b^2}{\displaystyle \eta+{}_{\ddots}}}}}$$ enjoying attractive algebraic properties such as a striking arithmetic-geometric mean relation and elegant connections with elliptic-function theory. But the fraction also presents an intriguing computational challenge. Herein we show how to rapidly evaluate ${\cal R}$ for any triple of positive reals $a,b,\eta$, the problematic scenario being when $a \approx b$, although even in such cases certain transformations allow rapid evaluation. In this process we find, for example, that when $a = b = $ rational, ${\cal R}_\eta$ is essentially an $L$-series that can be cast therefore as a finite sum of fundamental numbers. We ultimately exhibit an algorithm that yields $D$ good digits of ${\cal R}$ in $O(D)$ iterations where the implied big-$O$ constant is independent of the positive-real triple $a,b,\eta$. Finally, we address the evidently profound theoretical and computational dilemmas that arise when the parameters are allowed to become complex.

MEMBERSHIP

Membership to CARMA offers many benefits and is available by invitation to all University of Newcastle academic staff. Associate membership, also by invitation, is available to external researchers and practitioners for three-year renewable terms. Associate members are expected to visit CARMA with some frequency, typically for a total of three to four weeks in a year, and to be involved in one or more ongoing research projects with CARMA members. CARMA is able to assist with the travel and living costs of such visits.