# Issue 92, 30 September 2010

Featuring

'How and How Not to Compute the Exponential of a Matrix' - Watch Keynote

At a recent NAG Technical Event Professor Nicholas Higham FRS presented the keynote: 'How and How Not to Compute the Exponential of a Matrix'. NAG has worked closely with Professor Higham to create additional routines based on his work and they will be included in the next release of the NAG Library. Previous collaborative work with Professor Higham and NAG includes routines for calculating the Nearest Correlation Matrix http://www.nag.co.uk/IndustryArticles/Nearest_Correlation_Matrix.pdf and http://www.nag.co.uk/Market/nagquantday2009_ComputingaNearestCorrelationMatrixNickHigham.pdf.

How and How Not to Compute the Exponential of a Matrix Abstract

The matrix exponential, first introduced by Laguerre in 1867, is the most studied matrix function after the matrix inverse. It arises in many applications and a large literature exists on methods for computing it. Most of these methods are of limited practical use, due to their computational cost or numerical instability, but nevertheless some efficient and reliable methods are available. I will outline the history, applications and properties of the matrix exponential, and also its Frechet derivative, and describe a selection of computational methods-some good, some bad. In particular, I will discuss recent work on the problem of computing the action of the matrix exponential on a vector.

View the presentation

Partial Least Squares in the recently updated NAG C Library

Following on from the last edition of NAGNews where we highlighted a mini article on copula functions in the NAG C Library, today we focus on the Partial Least Squares functionality which is also new at Mark 9.

"Regression by means of projections to latent structures (PLS, also known as Partial Least Squares) is a useful alternative to the linear multiple regression model fitted by least squares if at least one of the following conditions applies:

- the x-variables, often known as predictors, are correlated;
- the number of x-variables is relatively high compared with the number of observations;
- the y-variable(s), often known as response(s), are correlated.

Thus the PLS method is popular in industries that collect correlated predictor data, for example, multivariate calibration in analytical chemistry; spectroscopy in chemometrics; and quantitative structure activity relationships in drug design."

Finish the article here.

NAG joins Demandtec Retail Challenge to encourage maths and science for high school students

We're delighted to be a sponsor of the Demandtec Retail Challenge. This unique maths and science competition, now in its fifth year, encourages high school students to apply their skills to pricing and inventory simulations, typical of real life situations. The competition culminates in the winning school team ringing the NASDAQ OMX Stock Market closing bell on 10th January 2011 in New York plus a monetary scholarship towards the college of their choice.

Rob Meyer, NAG CEO is currently pulling together teams from high schools in the Chigaco area, who will compete against other teams from San Francisco, Boston, Minneapolis, Pittsburgh and New York to make it to the final.

Students will get the opportunity to understand (and put into action) how retailers make pricing, inventory and marketing decisions.

John Ashworth Nelder (8 October 1924 - 7 August 2010)

We were saddened to learn that John Nelder passed away on 7 August 2010. John's contributions to the field of statistics while at Rothamstead and Imperial College were great, and he will be long remembered for his work. NAG is proud that he was a company member, a member of the former NAG Technical Policy Committee and was able to make it to the NAG 40 Anniversary celebrations in May this year.

We refer to an obituary by Roger Payne at VSN International.

Supercomputing: Is power-hungry supercomputing OK now?

The world's most powerful supercomputers can require many megawatts of electricity to operate. But what if the next factor of 1,000-fold performance increase needs 100MW, asks Andrew Jones, VP HPC Business at NAG.

I was recently interviewed about deploying the world's largest supercomputers for The Exascale Report, a magazine focused on the evolution of supercomputing and the targeted 1,000-fold increase in compute power in the next 10 years.

Inevitably the interview covered the huge costs and especially energy. It got me thinking. What follows is not yet my opinion - but it might start an interesting discussion.

There are a range of estimates for the likely power consumption of the first exaflops supercomputers, which are expected at some point between 2018 and 2020. But probably the most accepted estimate is 120MW, as set out in the Darpa Exascale Study edited by Peter Kogge (PDF).

At this figure, the supercomputing community panics and says it is far too much - we must get it down to between 20MW and 60MW, depending who you ask - and we worry even that is too much. But is it?

Read the full story in ZDNet

Recent Blog Posts

• HECToR User Group Meeting 2010 / XT6 Workshop
12-13 October, Manchester
NAG's HECToR dCSE team will be attending and presenting at the annual HECToR User Group Meeting and following XT6 Workshop

• Risk USA
1-4 November 2010, New York.
NAG will once again be exhibiting at the USA's premier risk management event for financial institutions.

• Quant Congress Europe
9-11 November 2010, London
NAG will be present at the event that reveals the most cutting edge research and innovations in market risk management, derivatives modelling and trading.

• SC10
15-18 November 2010, New Orleans
Multiple NAG experts will be attending this key event

• HECToR (High End Computing Terascale Resource) Training Courses
Presented by the NAG HECToR Team
A full list of forthcoming HECToR Training Courses can be viewed on the official HECToR website here.

New NAG product implementations

The NAG Toolbox for MATLAB®, Mark 22 is now also available for the following platforms:

• AMD-64 Windows64 for MATLAB (R2009b) or later

The NAG Fortran Compiler, Release 5.2 is now also available for the following platforms:

• Sun SPARC Solaris (gcc 3.4.2)
• Itanium Linux64

For full details of these and all other available implementations, visit http://www.nag.co.uk/. Comprehensive technical details of each implementation are given in the relevant Installer's and Users' Notes at http://www.nag.co.uk/doc/inun.asp

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