Multivariate Approximation and Interpolation with Applications

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Multivariate Approximation and Interpolation with Applications

 06 - 10 Sep 2010


Scientific Organisers

  • Oleg Davydov , University of Strathclyde
  • Tim Goodman, 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)

Speakers and their talk tiltes


Babenko, Yuliya

Sharp asymptotics of the error of adaptive approximation and interpolation by some classes of splines


Baxter, Brad

Exponential functionals of Brownian motion and approximation theory: a surprising link


Beatson, Rick

Preconditioning radial basis function interpolation problems


Berdysheva, Elena

Bernstein-Durrmeyer operators with general weight functions


Binev, Peter

Greedy algorithms for the Reduced Basis Method


Carnicer, Jesús

Remarks on the progressive iteration approximation property


Conti, Costanza

Non-stationary subdivision schemes and their reproduction properties


Dekel, Shai

Anisotropic representations and function spaces


Dyn, Nira

Geometric subdivision schemes


Floater, Michael

A piecewise polynomial approach to analyzing interpolatory subdivision


Han, Bin

Multivariate nonhomogeneous framelets and directional representation


Hangelbroek, Thomas

Approximation and interpolation on manifolds with kernels


Hesse, Kerstin

Smoothing approximation on the sphere from noisy scattered data


Hormann, Kai

On the Lebesgue constant of barycentric rational interpolation


Manni, Carla

Isogeometric analysis beyond NURBS


Nürnberger, Günther

Local Lagrange interpolation by splines on tetrahedral partitions


Peña, Juan Manuel

Accuracy, stability and applications to CAGD


Reif, Ulrich

Multivariate polynomial interpolation on approximation


Ron, Amos

Nonlinear approximation using surface splines and Gaussians


Rossini, Milvia

The detection and recovery of discontinuity curves from scattered data


Sabin, Malcolm

Geometric precision


Sablonnière, Paul

C1 and C2 bivariate LB-splines and associated interpolants


Sampoli, Maria Lucia

On a class of surfaces for geometric modeling


Sauer, Tomas

Hermite subdivision and factorization


Schaback, Robert

Bases for spaces of translates of kernels


Schumaker, Larry

Spline spaces on TR-meshes with hanging vertices


Speleers, Hendrik

Constructing a normalized basis for splines on Powell-Sabin triangulations


Stöckler, Joachim

Construction of frames for multivariate subdivision schemes


Wallner, Johannes

Multivariate data in manifolds: subdivision and derived operations


Ward, Joe

A new paradigm for RBF and SBF error estimates