Approximation Algorithms for Complex Systems: Proceedings of the 6th International Conference on Algorithms for Approximation, Ambleside, UK, 31st August - 4th September 2009

319 Pages·2011·3.33 MB·English

by  Darryl P. Almond

Springer Proceedings in Mathematics
Volume 3
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Emmanuil H. Georgoulis (cid:129) Armin Iske
Jeremy Levesley
Editors
Approximation Algorithms
for Complex Systems
Proceedings of the 6th International
Conference on Algorithms
for Approximation, Ambleside, UK,
August 31st – September 4th, 2009
123
Editors
EmmanuilH.Georgoulis JeremyLevesley
UniversityofLeicester UniversityofLeicester
DepartmentofMathematics DepartmentofMathematics
LeicesterLE17RH,UK LeicesterLE17RH,UK
[email protected] [email protected]
ArminIske
UniversityofHamburg
DepartmentofMathematics
D-20146Hamburg, Germany
[email protected]
ISSN2190-5614
ISBN978-3-642-16875-8 e-ISBN978-3-642-16876-5
DOI10.1007/978-3-642-16876-5
SpringerHeidelbergDordrechtLondonNewYork
MathematicsSubjectClassification(2010):65Dxx,65D15,65D05,65D07
(cid:2)c Springer-VerlagBerlinHeidelberg2011
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Preface
It appears that the role of the mathematician is changing, as the world re-
quires sophisticated tailored solutions to specific problems. Approximation
methods are of vital importance in many of these problems, as we usually do
not have perfect information, but require means by which robust solutions
can be garnered from complex and often evolutionary situations. This book
collects papers from world experts in a broad variety of relevant applications
of approximation theory, including dynamical systems, multiscale modelling
of fluid flow, metrology, and geometric modelling to mention a few.
The 14 papers in this volume document modern trends in approximation
through recent theoretical developments, important computational aspects
andmultidisciplinaryapplications.The bookis arrangedinseveninvitedsur-
veys, followed by seven contributed research papers. The surveys of the first
seven chapters are addressing the following relevant topics.
Emergent behaviour in large electrical networks
by Darryl P. Almond, Chris J. Budd, and Nick J. McCullen;
Algorithms for multivariate piecewise constant approximation
by Oleg Davydov;
Anisotropic triangulation methods in adaptive image approximation
by Laurent Demaret and Armin Iske;
Form assessment in coordinate metrology
by Alistair B. Forbes and Hoang D. Minh;
Discontinuous Galerkin methods for linear problems
by Emmanuil H. Georgoulis;
A numerical analyst’s view of the lattice Boltzmann method
by Jeremy Levesley, Alexander N. Gorban, and David Packwood;
Approximation of probability measures on manifolds
by Jeremy Levesley and Xingping Sun.
Moreover,the diverse contributed papers of the remaining seven chapters
reflect recent developments in approximation theory, approximation practice
VI Preface
and their applications. Graduate students who wish to discover the state of
the art in a number of important directions of approximationalgorithms will
findthisavaluablevolume.Establishedresearchersfromstatisticiansthrough
to fluid modellers will find interesting new approachesto solving familiar but
challenging problems.
This book grewoutofthe sixth inthe conferenceserieson Algorithmsfor
Approximation,whichtookplace from31stAugustto September 4th2009in
Ambleside in the Lake District of the United Kingdom. The conference was
supportedbytheEPSRC(GrantEP/H018026)andtheLondonMathematical
Society, and had around 70 delegates from 20 different countries.
The conference included also two workshops, the Model Reduction Work-
shop and New Mathematics for the Computational Brain. The papers of the
first workshop are appearing in a Springer volume Coping with Complexity:
Model Reduction and Data Analysis (Lecture Notes in Computational Sci-
enceandEngineering,Vol.75,Nov29,2010),editedbyAlexanderN.Gorban
and Dirk Roose, and the second as a special issue of International Journal of
NeuralSystems,Vol.20,No.3(2010).Theinteractionbetweenapproximation
theory,modelreduction,andneuroscience,wasveryfruitful,andresultedina
number of new projects which would never happened without collecting such
a broad-based group of people.
Finally, we are grateful to all the authors who have submitted their fine
papers for this volume, especially for their patience with the editors. The
contributions to this volume have all been refereed, and thanks go out to
all the referees for their timely and considered comments. Finally, we very
much appreciate the cordial relationship we have had with Springer-Verlag,
Heidelberg, through Martin Peters.
Leicester, August 2010 Emmanuil H. Georgoulis
Armin Iske
Jeremy Levesley
Contents
Part I Invited Surveys
Emergent Behaviour in Large Electrical Networks
Darryl P. Almond, Chris J. Budd, Nick J. McCullen ................. 3
Algorithms and Error Bounds for Multivariate Piecewise
Constant Approximation
Oleg Davydov.................................................... 27
Anisotropic Triangulation Methods in Adaptive Image
Approximation
Laurent Demaret, Armin Iske...................................... 47
Form Assessment in Coordinate Metrology
Alistair B. Forbes, Hoang D. Minh ................................. 69
Discontinuous Galerkin Methods for Linear Problems:
An Introduction
Emmanuil H. Georgoulis .......................................... 91
A Numerical Analyst’s View of the Lattice Boltzmann
Method
Jeremy Levesley, Alexander N. Gorban, David Packwood ..............127
Approximating Probability Measures on Manifolds via Radial
Basis Functions
Jeremy Levesley, Xingping Sun ....................................151
Part II Contributed Research Papers
Modelling Clinical Decay Data Using Exponential Functions
Maurice G. Cox .................................................183
VIII Contents
Towards Calculating the Basin of Attraction of Non-Smooth
Dynamical Systems Using Radial Basis Functions
Peter Giesl......................................................205
Stabilizing Lattice Boltzmann Simulation of Fluid Flow past
a Circular Cylinder with Ehrenfests’ Limiter
Tahir S. Khan, Jeremy Levesley ...................................227
Fast and Stable Interpolation of Well Data Using the Norm
Function
Brian Li, Jeremy Levesley ........................................241
Algorithms and Literate Programs for Weighted Low-Rank
Approximation with Missing Data
Ivan Markovsky..................................................255
On Bivariate Interpolatory Mask Symbols, Subdivision
and Refinable Functions
A. Fabien Rabarison, Johan de Villiers .............................275
Model and Feature Selection in Metrology Data
Approximation
Xin-She Yang, Alistair B. Forbes ..................................293
List of Contributors
Darryl P. Almond Emmanuil H. Georgoulis
Bath Institutefor Complex Systems University of Leicester
University of Bath Department of Mathematics
Bath BA2 7AY,UK Leicester LE1 7RH, UK
[email protected] [email protected]
Peter Giesl
Chris J. Budd
University of Sussex
Bath Institutefor Complex Systems
Department of Mathematics
University of Bath
Falmer BN1 9QH,UK
Bath BA2 7AY,UK
[email protected]
[email protected]
Alexander N. Gorban
Maurice G. Cox University of Leicester
National Physical Laboratory Department of Mathematics
Teddington TW11 0LW, UK Leicester LE1 7RH, UK
[email protected] [email protected]
Oleg Davydov Armin Iske
University of Strathclyde University of Hamburg
Dept of Mathematics and Statistics Department of Mathematics
Glasgow G1 1XH, UK D-20146 Hamburg, Germany
[email protected] [email protected]
Tahir S. Khan
Laurent Demaret
University of Leicester
HelmholtzZentrum mu¨nchen
Department of Mathematics
Institutefor Biomathematics
Leicester LE1 7RH, UK
Neuherberg, Germany
[email protected]
[email protected]
Jeremy Levesley
Alistair B. Forbes University of Leicester
National Physical Laboratory Department of Mathematics
Teddington TW11 0LW, UK Leicester LE1 7RH, UK
[email protected] [email protected]