Abstract
The fourth conference on “Multivariate Approximation: Theory and Applications” was held April 26 to May 01, 2007 at Cancun, Mexico. This introductory paper describes the main topics in Approximation Theory presented during this conference, ranging from theoretical aspects to numerous applications.
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References
As references, we give here the title of every talk of the conference. Those in boldface are published in the form of a paper in this issue.
Ablamowicz, R.: Computational algebraic geometry methods for curves and surfaces.
Arcangéli, R., Lopez de Silanes, M.C., Torrens, J.J.: An extension of a bound for functions in Sobolev spaces and its application to (m, s) spline interpolation and smoothing.
Auquiert, P., Gibaru, O., Nyiri, E.: C1 and C2-continuous polynomial parametric L p splines (p ≥ 1).
Corrochano, E.B.: Applications of quaternion wavelet transform: for robotic vision.
Bozzini, M.: A local method for large and unevenly distributed data.
Buhmann, M.: Radial basis function interpolation with parameters.
Casarrubias, H., Sossa, H., Barrón, R.: Using cubic spline for the velocity planning in mobile robots.
Charleston-Villalobos, S., Cruz-García, J., González-Camarena, R., Aljama-Corrales, T.: Forward and inverse problems for determining computer simulated respiratory sound sources.
Cisneros, H., Barrón, R., Cruz, B.: Isolated character recognition by using Support Vector Machines with a kernel of radial base.
Cruz, B., Barrón, R., López, J., Sossa, H.: Some formal aspects and applications of Cartan Dieudonné theorem.
Dadourian, K., Liandrat, J.: Analysis of some bivariate non-linear interpolatory subdivision schemes and associated multiresolution.
Damelin, S.B.: A walk through energy, discrepancy, numerical integration and group invariant measures on measurable subsets of Euclidean space.
Dechevsky, L.T.: Expo-rational B-splines of a complex variable and their applications.
Dechevsky, L.T., Bang, B., Bu, XF, Lakså, A.: Variational calculus and multigrid dynamical programming on expo-rational surfaces and volume deformations: theory and applications.
Dechevsky, L.T., Lakså, A., Bang, B.: Generalized expo-rational B-splines.
De Knock, B., Brackx, F., De Schepper, H.: A new Hilbert transform in a metric dependent Clifford setting.
Falcon, L.E., Bayro-Corrochano, E.: Radon transform and harmonical analysis for 3D motion estimation using robot omnidirectional vision.
Forcadel, N., Le Guyader, C., Gout, C.: Image segmentation using a generalized fast marching method.
González-Casanova, P., Gómez, J.A.M., Gómez, G.R.: A dynamical node adaptive RBF method to solve PDE problems.
Gout, C., Le Guyader, C.: Geodesic active contour under geometrical conditions: theory and 3D applications.
Grebennikov, A., Luna, J.G.V., Perez, T.V., Enriquez, M.N.: Rotating projection algorithm of image reconstruction and application for computer tomography.
Gürlebeck, K.: On monogenic approximations of solutions of the Lamé system.
Hernandez, V., del Agel, P.L., Estrada, J.: Umbrella based triangulation of regular parametric surfaces.
Hoffmann, M., Juhasz, I.: General formulae of B-spline curves with shape parameters.
Jaklic, G., Kozak, J., Krajnc, M., Vitrih, V., Zagar, E.: Lattices on simplices.
Juarez, L.H.: Numerical simulation of a viscous pump by a high order finite element method.
Kunoth, A.: Fast multiscale methods for PDE-constrained control problems.
Le Guyader, C., Vese, L.: Self-repelling snakes for topology-preserving segmentation model.
Levesley, J.: The order of approximation of transport equations by the kinetic equation.
Mhaskar, H.N.: Diffusion polynomial frames on metric measure spaces.
Mørken, K.: Mathematical and computational challenges in some applications of medical imaging.
Neamtu, M.: Splines for surfaces of arbitrary topology.
Pitolli, F.: Sparse approximation for source separation in the magnetoencephalography inverse problem.
Rabut, C.: How to reduce Runge phenomenon.
Reséndiz, R.: Building solids using quaternions.
Rossini, M.: Polyharmonic B-splines.
Saint-Guirons, A.-G., Gout, C., Le Guyader, C., Romani, L.: Surface approximation of surfaces with fault(s) and/or rapidly varying data, using a segmentation process, Dm-splines and the finite element method.
Schumaker, L.: A C1 quadratic trivariate macro-element space defined over arbitrary tetrahedral partitions.
Sommen, F.: The Dirac equation for bivector mass.
Sproessig, W.: Hyperholomorphic functions in elasticity and fluid dynamics.
Steidl, G.: Diffusion filters and wavelets.
Toscano, K., Barrón, R., Sossa, H.: Hand-written character recognition using spline wavelets.
Traversoni, L.: Wavelets and movements: different approaches.
Van de Voorde, L., De Schepper, H., Sommen, F.: Some results in discrete Clifford analysis.
Vese, L.: Variational image decomposition models into cartoon and texture.
Waldron, S.: Tight frames and their symmetries.
Xu, Y.: QWT: retrospective and new applications.
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de Boor, C., Gout, C., Kunoth, A. et al. Multivariate approximation: theory and applications. An overview. Numer Algor 48, 1–9 (2008). https://doi.org/10.1007/s11075-008-9190-y
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DOI: https://doi.org/10.1007/s11075-008-9190-y