Multivariate Approximation and Interpolation with Applications

Scientific Organisers

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

About:

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