Entrance hall of the ICMS Workshop

Multivariate Approximation and Interpolation with Applications

Sep 06, 2010 - Sep 10, 2010

15 South College Street, Edinburgh EH8 9AA

Organisers

Name Institution
Davydov, Oleg University of Strathclyde
Goodman, Tim University of Dundee

Approximation theory has evolved from classical work by Chebyshev, Weierstrass and Bernstein into an area that combines a deep theoretical analysis of approximation with insights leading to the invention of new computational techniques. Such invaluable tools of modern computation as orthogonal polynomials, splines, finite elements, Bézier curves, NURBS, radial basis functions, wavelets and subdivision surfaces have been developed and analysed with the prominent help of ideas coming from approximation theory.

The workshop is devoted to the approximation of functions of two or more variables. This area has many challenging open questions and its wide variety of applications includes problems of computer aided design, mathematical modelling, data interpolation and fitting, signal analysis and image processing.

The focus will be on the following research topics:
• Approximation and interpolation with multivariate polynomials, splines, and radial basis functions.
• Linear and non-linear subdivision.
• Adaptive and multiresolution methods of approximation.
• Shape preserving approximation.

Scientific Advisory Group

Carl de Boor (University of Wisconsin-Madison, USA)
Mira Bozzini (University of Milan, Italy)
Paolo Costantini (University of Siena, Italy)
Nira Dyn (University of Tel Aviv, Israel)
Mariano Gasca (University of Zaragoza, Spain)
Kurt Jetter (University of Stuttgart-Hohenheim, Germany)
Tom Lyche (University of Oslo, Norway)
Alistair Watson (University of Dundee, UK)

PDF file of full report.

Arrangements

Participation
Participation is by invitation only. People interested in participating should contact the organisers. The workshop will begin on Monday 6 September and finish on Friday 10 September 2010.

UK Visas
If you are travelling from overseas you may require an entry visa. A European visa does not guarantee entry to the UK. Please use this link to the UK Visas site to find out if you need a visa and, if so, how to apply for one. If you do require a visa, ICMS can (on request) provide a signed invitation letter.

Venue
The workshop will be held at 15 South College Street, Edinburgh. All lectures will be held in the Newhaven Lecture Theatre. To view this room and a list of the visual equipment available click here. In addition, two blackboards have recently been installed and a PC outputting to a high definition projector and audio system. Follow this link for a map showing the location of 15 South College Street. This map may also prove useful. 

Accommodation
ICMS will arrange en-suite rooms in hotels/ university accommodation nearby for those who request this. Accommodation is typically about 10 to 20 minute walk from 15 South College Street. Participants making their own arrangements may claim back the cost, with original receipts, up to a maximum of £55.00 per night bed and breakfast for a maximum of six nights. A list of Edinburgh accommodation of various sorts and prices is available here. Sections 3-4 are particularly relevant.

Wireless Access
The workshop venue, 15 South College Street, has wireless access throughout. On arrival at Registration you will be given instructions and a code for accessing the wireless network. For those without laptops, there will also be a couple of computers available for you to check your emails.

Travel
Information about travel to the UK and Edinburgh is available here. Lothian buses charge 1.20 GBP for a single journey and 3.00 GBP for a day ticket. Please note that the exact fare is required and no change is given.

A taxi directly from the airport will cost approximately 18.00 to 20.00 GBP to the city centre for a one-way journey.

From the airport, you can take the airport bus Airlink to the city centre. It will cost you 3.50 GBP for a single ticket, or 6.00 GBP return. More details on the airport bus Airlink is available here. The bus will take you to Waverley Bridge (next to Waverley Railway Station).

If travelling by train, please note that Edinburgh has two railway stations - Waverley Railway Station being the main station and closest to the workshop venue at 15 South College Street. If you alight at Edinburgh Waverley, the workshop venue is an easy 10 minute walk over North and South Bridge map. The second railway station is called Haymarket and is at the West End of the city centre. 

Please note that it is your responsibility to have adequate travel insurance to cover medical and other emergencies that may occur on your trip.

Catering
Morning and afternoon refreshments will be provided on each day of the workshop.

Buffet lunch will be provided in the Chapterhouse on the ground floor of 15 South College Street on Monday 6 September only.

The workshop dinner will take place on the evening of Thursday 9 September in The Magnum Restaurant, 1 Albany Street, Edinburgh, EH1 3PY.

The workshop grant will cover the cost of this catering for workshop participants.

Coach Trip to Rosslyn Chapel
On Wednesday 8 September there will be a coach trip to Rosslyn Chapel from 15.00–19.00. This will be free of charge to participants. Registration for the excursion will take place on Monday.

At 14.45 we will assemble for a 3-minute walk to Appleton Tower on Crighton Street to board our coach, which will leave promptly at 15.00, for a 30 minute coach journey to Rosslyn Chapel. This extraordinary building dates back to 1446. The architecture, stone carvings and history draw visitors from all over the globe. A guided tour of the Chapel is arranged for 16.00 and will last approximately 30-40 minutes. There will then be time to wander round the Chapel grounds or visit the Exhibition Room and shop before boarding the coach [at 18.30] for a return to Edinburgh around 19.00. Please note that, on our return, there will be no access to the building at 15 South College Street. 

Registration
Registration will take place 08.30 - 09.30 on Monday 6 September at 15 South College Street, Edinburgh. 

Financial Arrangements
Due to budget restrictions, we ask that you cover the cost of your own travel if possible. Your individual financial arrangements will be laid out in your invitation and repeated in your final email, which will be sent shortly before the workshop. If we have agreed to pay some of your travel costs, you will be informed by email. Reimbursement will take place after the workshop and will involve payment directly into your bank account. At Registration you will be given an expenses claim form and this should be submitted to ICMS, with original receipts. It would be helpful if you could bring your bank details to the workshop. In addition to the bank account number, participants from the USA and Canada will require their bank’s routing number, those from the UK will be asked for the bank sort code, and those from Europe and the rest of the world, their IBAN and SWIFT/BIC code. We cannot reimburse any item without a signed claim form and original receipts. 

Unless otherwise stated in your invitation email, there will be a registration fee of 30.00 GBP for the workshop. We ask that this is paid in advance by using this credit or debit card payment form. The form should be printed out, completed and faxed back (as email is not a secure way of sending credit card information). The fax number is on the form. If it is not possible for you pay in advance, you may print out the credit/debit card form above and bring the completed form along to Registration. We prefer not to handle cash at Registration.

 

Programme

Provisional Programme

Monday 6 September

08.30 - 09.30

Registration and coffee in the Chapterhouse, Ground Floor, 15 South College Street

 

Morning chairperson: Larry Schumaker

09.30 - 10.15

Nira Dyn (Tel Aviv University)
Geometric subdivision schemes

10.15 - 11.00

Johannes Wallner (TU Graz)
Multivariate data in manifolds: subdivision and derived operations

11.00 - 11.30

Coffee/Tea

11.30 - 12.15

Michael Floater (University of Oslo)
A piecewise polynomial approach to analyzing interpolatory subdivision

12.15 - 13.00

Joachim Stöckler (University of Dortmund)
Construction of frames for multivariate subdivision schemes

13.00 - 14.00

Lunch provided in the Chapterhouse (ground floor)

 

Afternoon chairperson: Carl de Boor

14.00 - 14.45

Amos Ron (University of Wisconsin-Madison)
Non linear approximation using surface splines and Gaussians

14.45 - 15.30

Thomas Hangelbroek (Vanderbilt University)
Approximation and interpolation on manifolds with kernels

15.30 - 16.00

Coffee/Tea

16.00 - 16.45

Milvia Rossini (University of Milan)
The detection and recovery of discontinuity curves from scattered data

 

Tuesday 7 September

 

Morning chairperson: Tom Lyche

09.00 - 09.45

Larry Schumaker (Vanderbilt University)
Spline spaces on TR-meshes with hanging vertices

09.45 - 10.30

Günther Nürnberger (University of Mannheim)
Local Lagrange interpolation by splines on tetrahedral partitions

10.30 - 11.00

Coffee/Tea

11.00 - 11.45

Paul Sablonnière (INSA de Rennes)
C1 and C2 bivariate LB-splines and associated interpolants

11.45 - 12.30

Hendrik Speleers (Katholieke Universiteit Leuven)
Constructing a normalized basis for splines on Powell-Sabin triangulations

12.30 - 14.00

Lunch break

 

Afternoon chairperson: Nira Dyn

14.00 - 14.45

Malcolm Sabin (Numerical Geometry Ltd)
Geometric precision

14.45 -15.30

Costanza Conti (University of Florence)
Non-stationary subdivision schemes and their reproduction properties

15.30 - 16.00

Coffee/Tea

16.00 - 16.45

Tomas Sauer (University of Giessen)
Hermite subdivision and factorization

 

Wednesday 8 September

 

Morning chairperson: Mike Powell

09.00 - 09.45

Robert Schaback (University of Göttingen)
Bases for spaces of translates of kernels

09.45 - 10.30

Rick Beatson (University of Canterbury)
Preconditioning radial basis function interpolation problems

10.30 - 11.00

Coffee/Tea

11.00 - 11.45

Joe Ward (Texas A&M University)
A new paradigm for RBF and SBF error estimates

11.45 - 12.30

Kerstin Hesse (University of Sussex)
Smoothing approximation on the sphere from noisy scattered data

15.00 - 19.00

Coach trip to Rosslyn Chapel, Midlothian. See further details above.

 

Thursday 9 September

 

Morning chairperson: Carla Manni

09.00 - 09.45

Ulrich Reif (University of Darmstadt)
Multivariate polynomial interpolation on approximation

09.45 - 10.30

Elena Berdysheva (University of Hohenheim)
Bernstein-Durrmeyer operators with general weight functions

10.30 - 11.00

Coffee/Tea

11.00 - 11.45

Juan Manuel Peña (Universidad de Zaragoza)
Accuracy, stability and applications to CAGD

11.45 - 12.30

Kai Hormann (University of Lugano)
On the Lebesgue constant of barycentric rational interpolation

12.30 - 14.00

Lunch break

 

Afternoon chairperson: Kurt Jetter

14.00 - 14.45

Jesús Carnicer (Universidad de Zaragoza)
Remarks on the progressive iteration approximation property

14.45 - 15.30

Brad Baxter (University of London)
Exponential functionals of Brownian motion and approximation theory: a surprising link

15.30 - 16.00

Coffee/Tea

19.00 -

Workshop Dinner - The Magnum Restaurant, 1 Albany Street, Edinburgh 

 

Friday 10 September

 

Afternoon chairperson: Alistair Watson

09.00 - 09.45

Carla Manni (University of Roma "Tor Vergata")
Isogeometric analysis beyond NURBS

09.45 - 10.30

Maria Lucia Sampoli (University of Siena)
On a class of surfaces for geometric modeling

10.30 - 11.00

Coffee/Tea

11.00 - 11.45

Shai Dekel (Tel-Aviv University & GE-Healthcare)
Anisotropic representations and function spaces

11.45 - 12.30

Yuliya Babenko (Kennesaw State University)
Sharp asymptotics of the error of adaptive approximation and interpolation by some classes of splines

12.30 - 14.00

Lunch break

 

Afternoon chairperson: Martin Buhmann

14.00 - 14.45

Peter Binev (University of South Carolina)
Greedy algorithms for the Reduced Basis Method

14.45 - 15.30

Bin Han (University of Alberta)
Multivariate nonhomogeneous framelets and directional representation

15.30 - 16.15

Coffee/Tea

 

Presentations:

Presentation Details
Babenko, Yuliya
Sharp asymptotics of the error of adaptive approximation and interpolation by some classes of splines
View Abstract Down
Baxter, Brad
Exponential functionals of Brownian motion and approximation theory: a surprising link
View Abstract Down
Beatson, Rick
Preconditioning radial basis function interpolation problems
View Abstract Down
Berdysheva, Elena
Bernstein-Durrmeyer operators with general weight functions
View Abstract Down
Binev, Peter
Greedy algorithms for the Reduced Basis Method
View Abstract Down
Carnicer, Jesús
Remarks on the progressive iteration approximation property
View Abstract Down
Conti, Costanza
Non-stationary subdivision schemes and their reproduction properties
View Abstract Down
Dekel, Shai
Anisotropic representations and function spaces
View Abstract Down
Dyn, Nira
Geometric subdivision schemes
View Abstract Down
Floater, Michael
A piecewise polynomial approach to analyzing interpolatory subdivision
View Abstract Down
Han, Bin
Multivariate nonhomogeneous framelets and directional representation
View Abstract Down
Hangelbroek, Thomas
Approximation and interpolation on manifolds with kernels
View Abstract Down
Hesse, Kerstin
Smoothing approximation on the sphere from noisy scattered data
View Abstract Down
Hormann, Kai
On the Lebesgue constant of barycentric rational interpolation
View Abstract Down
Manni, Carla
Isogeometric analysis beyond NURBS
View Abstract Down
Nürnberger, Günther
Local Lagrange interpolation by splines on tetrahedral partitions
View Abstract Down
Peña, Juan Manuel
Accuracy, stability and applications to CAGD
View Abstract Down
Reif, Ulrich
Multivariate polynomial interpolation on approximation
View Abstract Down
Ron, Amos
Nonlinear approximation using surface splines and Gaussians
View Abstract Down
Rossini, Milvia
The detection and recovery of discontinuity curves from scattered data
View Abstract Down
Sabin, Malcolm
Geometric precision
View Abstract Down
Sablonnière, Paul
C1 and C2 bivariate LB-splines and associated interpolants
View Abstract Down
Sampoli, Maria Lucia
On a class of surfaces for geometric modeling
View Abstract Down
Sauer, Tomas
Hermite subdivision and factorization
View Abstract Down
Schaback, Robert
Bases for spaces of translates of kernels
View Abstract Down
Schumaker, Larry
Spline spaces on TR-meshes with hanging vertices
View Abstract Down
Speleers, Hendrik
Constructing a normalized basis for splines on Powell-Sabin triangulations
View Abstract Down
Stöckler, Joachim
Construction of frames for multivariate subdivision schemes
View Abstract Down
Wallner, Johannes
Multivariate data in manifolds: subdivision and derived operations
View Abstract Down
Ward, Joe
A new paradigm for RBF and SBF error estimates
View Abstract Down

Participants

Name Institution
Andriamaro, Gaelle University of Strathclyde
Babenko, Yuliya Kennesaw State University
Baxter, Brad University of London
Beatson, Rick University of Canterbury
Berdysheva, Elena University of Hohenheim
Binev, Peter University of South Carolina
Bozzini, Mira University of Milano Bicocca
Buhmann, Martin Justus-Liebig University
Carnicer, Jesús Universidad de Zaragoza
Chernih, Andrew University of New South Wales
Conti, Costanza University of Florence
Davydov, Oleg University of Strathclyde
de Boor, Carl University of Wisconsin-Madison
Dekel, Shai Tel-Aviv University & GE-Healthcare
Dyn, Nira Tel Aviv University
Floater, Michael University of Oslo
Goodman, Tim University of Dundee
Han, Bin University of Alberta
Hangelbroek, Thomas Vanderbilt University
Hesse, Kerstin University of Sussex
Hormann, Kai University of Lugano
Jetter, Kurt University of Hohenheim
Lyche, Tom University of Oslo
Manni, Carla University of Roma "Tor Vergata"
Merrien, Jean-Louis INSA de Rennes
Nürnberger, Günther University of Mannheim
Peña, Juan Manuel Universidad de Zaragoza
Powell, Mike University of Cambridge
Rabarison, Andrianarivo Fabien University of Strathclyde
Rabut, Christophe University of Toulouse
Reif, Ulrich University of Darmstadt
Reimers, Martin University of Oslo
Ron, Amos University of Wisconsin-Madison
Rossini, Milvia University of Milan
Sabin, Malcolm Numerical Geometry Ltd
Sablonnière, Paul INSA de Rennes
Sampoli, Maria Lucia University of Siena
Sauer, Tomas University of Giessen
Schaback, Robert University of Göttingen
Schumaker, Larry Vanderbilt University
Speleers, Hendrik Katholieke Universiteit Leuven
Stöckler, Joachim University of Dortmund
Tong, Robert Numerical Algorithms Group Ltd
Wallner, Johannes TU Graz
Ward, Joe Texas A&M University
Watson, Alistair University of Dundee
Yeo, Wee Ping University of Strathclyde