Numerical analysis and scientific computing are two of the fundamental areas in the study of methods, techniques, and algorithms for obtaining approximations to solutions of financial mathematical and physical problems. This workshop provides students and researchers with training in practical and effective approximation techniques, immediately applicable in a variety of contexts in research fields, based on two open-source software packages. Chebfun and ApproxFun are open-source packages for computing with functions. They aim to combine the convenient user experience of symbolic computing with the speed and efficiency of numerical methods. The syntax for Chebfun is almost exactly the same as the usual MATLAB syntax for vectors, with the familiar MATLAB commands for vectors overloaded in natural ways, allowing anyone familiar with the MATLAB language to immediately begin exploring. In 2012, Chebfun Version 5 provides an excellent environment for both newcomers and experts to explore. Moreover, since 2019, ApproxFun, written in Julia (a modern high-performance numerical programming language), is a package for approximating and manipulating functions, and for solving differential and integral equations. It is in a similar vein to the MATLAB package Chebfun and the Mathematica package RHPackage. There are significant amounts of good features in ApproxFun. One of them is to provide different spaces, indicating which space a function lives in, such as Chebyshev space, Ultraspherical space and the like, to solve functions. Because of this feasibility, this makes ApproxFun solve differential equations and the like more easily and accurately.

The two-day workshop rundown:

• Morning 1: Approximation theory and introduction to Chebfun/ApproxFun
• Lunch and refreshments provided
• Afternoon 1: Solving differential equations in Chebfun/Approxfun
• Morning 2: 2D multivariate approximation and PDEs
• Lunch and refreshments provided
• Afternoon 2: Applications

Registration:

The workshop is only organised for students at Queen Mary University of London and Imperial College London. Any students not from these two universities are required to send the organiser an email for special admission.

To register for the event on Eventbrite, attendees go to the event listing and click "Tickets". Then they choose their tickets, fill out their information, and place their order. Once an order completes, attendees receive an order confirmation email with their tickets attached.

Venue (online/on campus):

The workshop will be streamed online with Microsoft Teams and also held in the Mathematical Sciences Building MB-302 simultaneously.

The Microsoft Teams link will be announced close to the time.

The Mathematical Sciences Building on Queen Mary University of London's Mile End campus -see on this map.

For maps, directions, access information and travel guidance please click here.

Speakers:

Dr Sheehan Olver is the founder of Approxfun and a Reader in Applied Mathematics and Mathematical Physics at Imperial College London since 2017. Before joining Imperial College London, Dr. Olver was a Lecturer, Senior Lecturer and Associate Professor at The University of Sydney. Olver’s research interest focuses on numerical analysis and computational methods. He has developed spectral methods for ordinary and partial differential equations, singular integral equations, and Riemann–Hilbert problems, with applications in integrable systems and the study of random matrices.

Dr Nick Hale was the lead developer of Chebfun (part-funded by The MathWorks) for two years. He is an Associate Professor of Applied Mathematics at University of Stellenbosch since 2019. Prior to this appointment, Hale was Post-doctoral Research Fellow at the University of Oxford. Hale’s research focus is on numerical analysis, scientific computing, and computational software, in particular spectral methods for differential equations, fast algorithms for polynomial and related transforms, numerical solution of fractional differential equations, and numerical complex analysis.

Dr Ron Chan is a Lecturer in Mathematics at Queen Mary University of London. Prior to joining the School of Mathematical Finance, Chan was a Senior Lecturer in Finance at University of East London, a Risk Specialist at Standard & Poor’s (London) and a Software Engineer at IBM Global. Chan’s main research focuses on the domains of finance, machine learning, numerical methods and statistics. In one line of research, Chan applies numerical methods and machine learning techniques, mainly numerical linear algebra approaches, to derivatives pricing and hedging problems, value investment strategies and extremely large derivatives portfolio management. Recently, Chan has been involved using Chebfun in financial engineering.

Dr Marco Fasondini is a Research Associate at Imperial College London. Previously holding a postdoc at University of Kent, Fasondini’s research focuses spectral methods, orthogonal polynomials, differential equations in the complex plane.