Research: Ph.D.
For my Ph.D. I researched Monte Carlo methods for matrix computations. During this research I was part of the Centre for Advanced Computing and Emerging Technologies, in the School of Systems Engineering at the University of Reading..
This research was into developing algorithms to solve systems of linear algebraic equations and invert matrices, which are two problems of unquestionable importance in many scientific and engineering applications: e.g. real-time speech coding, digital signal processing, communications, stochastic modelling, and many physical problems involving partial differential equations.
In particular, I concentrated on:
- hybrid methods, which use Monte Carlo to quickly generate an approximate inverse matrix and then improve the approximation with deterministic refinement;
- parallel algorithms, which harness multiple processing elements to efficiently and effectively solve the problems;
- sparse matrices, since sparse problems are common in many of the scientific applications of these algorithms;
- sparse inverses, which use various techniques to ensure that the generated inverse matrix is sparse and, so, reduce the computational cost and memory requirements of the algorithm;
- resolvent methods, to produce an unbiased estimate of the inverse matrix or solution vector;
- iterative Monte Carlo schemes for solving systems of linear algebraic equations.
- hybrid methods, which use Monte Carlo to quickly generate a rough inverse and improving this with deterministic refinement;
Publications
Simon Branford. Hybrid Monte Carlo Methods For Linear Algebra Problems. PhD thesis, School of Systems Engineering, University of Reading, 2008.
Simon Branford, Cihan Sahin, Ashish Thandavan, Christian Weihrauch, Vassil Alexandrov, and Ivan Dimov. Monte Carlo methods for matrix computations on the grid. In Future Generation Computer Systems, Vol. 24(6):605-612 , 2007. doi:10.1016/j.future.2007.07.006
Christian Weihrauch, Ivan Dimov, Simon Branford, and Vassil Alexandrov. Comparison of the Computational Cost of a Monte Carlo and Deterministic Algorithm for Computing Bilinear Forms of Matrix Powers. In Computational Science – ICCS 2006, Vol. 3993:640 to 647 of Lecture Notes in Computer Science, Springer-Verlag, 2006. doi:10.1007/11758532_84
Ivan Dimov, Vassil Alexandrov, Simon Branford, and Christian Weihrauch. Error Analysis of a Monte Carlo Algorithm for Computing Bilinear Forms of Matrix Powers. In Computational Science – ICCS 2006, Vol. 3993:632 to 639 of Lecture Notes in Computer Science, Springer-Verlag, 2006. doi:10.1007/11758532_83
Simon Branford, Christian Weihrauch, and Vassil Alexandrov. A Sparse Parallel Hybrid Monte Carlo Algorithm for Matrix Computations. In Computational Science – ICCS 2005, Vol. 3516:743 to 751 of Lecture Notes in Computer Science, Springer-Verlag, 2005. doi:10.1007/11428862_101
Vassil Alexandrov, Emanouil Atanassov, Ivan Dimov, Simon Branford, Ashish Thandavan, and Christian Weihrauch. Parallel Hybrid Monte Carlo Algorithms for Matrix Computations. In Computational Science – ICCS 2005, Vol. 3516:752 to 759 of Lecture Notes in Computer Science, Springer-Verlag, 2005. doi:10.1007/11428862_102
Conferences and Workshops
June 2007: I was on the organising and programming committees for the Sixth International Association for Mathematics and Computers in Simulation seminar on Monte Carlo Methods (MCM2007) at the University of Reading.
June 2007: Sixth International Conference on Large-Scale Scientific Computations in Sozopol, Bulgaria.
May 2007: Seventh International Conference on Computational Science 2007 (ICCS2007) in Beijing, China.
November 2006: SC06 in Tampa, USA.
May 2006: I was on the organising and programming committees for the International Conference on Computational Science 2006 (ICCS2006) at the University of Reading.
July 2005: Grid’05 – a EGEE Summer School at MTA SZTAKI. At this I learnt about Grid technology and the EGEE infrastructure.
May 2005: International Conference on Computational Science 2005 (ICCS2005) at Emory University.
May 2005: Fifth International Association for Mathematics and Computers in Simulation seminar on Monte Carlo Methods (MCM2005) at Florida State University.
October 2004: Third international workshop on Parallel Matrix Algorithms and Applications (PMAA2004) and the workshop on Matrices in Statistics and Optimization (MSO2004) at Centre International de Rencontres Mathematiques. At this conference Prof. Vassil Alexandrov presented A new parallel hybrid Monte Carlo Algorithm for Matrix Computations, which is the research of Vassil, Christian Weihrauch, and myself.
Talks
20th June 2007, at the Sixth International Association for Mathematics and Computers in Simulation seminar on Monte Carlo Methods: Sparse Hybrid Monte Carlo Methods for Matrix Computations.
28th May 2007, at the International Conference on Computational Science 2007: Complexity of Monte Carlo Algorithms for a Class of Integral Equations.
23rd November 2005, for the ACET weekly seminars: Parallel Hybrid Monte Carlo Algorithms for Matrix Computations.
25th May 2005, at the International Conference on Computational Science 2005: A Sparse Parallel Hybrid Monte Carlo Algorithm for Matrix Computations.
19th May 2005, at the Fifth International Association for Mathematics and Computers in Simulation seminar on Monte Carlo Methods: A Comparison of Using Uniform and Almost Optimal Transition Probabilities in a Monte Carlo Algorithm for Matrix Computations.
Other
I was the webmaster for the ACET High Performance Computing and Visualization website. This site aims to be a single source of information relating to the description, use, and current status of computing resources at ACET.
I was part of the NATO Science Project # CLG. 982641: Monte Carlo Sensitivity Studies of Environmental Security, NATO Security Through Science programme, Collaboartive Linkage Grant. This was a joint project between ACET, the University of Reading, Reading, UK; CLPP, BAS, Sofia, Bulgaria and NERI, Roskilde, Denmark (Project Coordinator: I. Dimov; Project Coordinator from a Partner country: E. Atanassov; Principal Investigator: Z. Zlatev) (2007-2009).
I was the webmaster for the sixth International Association for Mathematics and Computers in Simulation seminar on Monte Carlo Methods – MCM2007. For this conference I developed and maintained a custom submission and registration system.
I taught both the lectures and practicals for Linear Algebra Part I and Part II in the Advanced European MSc in Network Centred Computing.
