UMR-CNRS Mathematics
APPROXIMATION PAPERS (University of Pau, France)
UMR-CNRS Mathematics
Multivariate polynomial interpolation (Interesting link >>> S. Waldron >>>)
A. Guessab and G. Schmeisser , Sharp error estimates for interpolatory approximation on convex polytopes , (SIAM Journal on Numerical Analysis 2005)
Guessab A.; Schmeisser G. , Sharp Integral Inequalities of the Hermite-Hadamard Type, Journal of Approximation Theory, April 2002, vol. 115, no. 2, pp. 260-288(29).
Arcangeli, Rémi; Gout, Jean-Louis. Sur l'interpolation de Lagrange dans $R\sp n$. C. R. Acad. Sci. Paris Sér. A-B 281 (1975), no. 10, Aii, A357--A359
Arcangéli, R.; Gout, J. L. Sur l'évaluation de l'erreur d'interpolation de Lagrange dans un ouvert de $R\sp{n}$. (French) Publications mathématiques de l'Université de Pau et des Pays de l'Adour (dédiées à Pierre Abile), Exp. No. 5, 22 pp. Univ. de Pau et des Pays de l'Adour, Pau, 1974.
Interpolation-Quadrature formulae
Gout, C.; Guessab, A. Extended lagrange interpolation and nonclassical Gauss quadrature formulae, Mathematical and Computer Modelling, vol. 38, no. 1-2, pp. 209-228 2003.
C. Gout, A. Guessab, A new family of Extended Gauss Quadratures with an Interior Constraint, Journal of Computational and Applied Mathematics, Vol 131/1-2, pp 35-53, 2001.
B. Bojanov, A. Guessab, Gaussian quadrature formula of Birhoff's type, Calcolo, Vol. 34, Nos1-4, pp. 41-50, 1997.
A. Ezzirani, A. Guessab, A fast algorithm for Gaussian type quadrature formulae with mixed boundary conditions and some lumped mass spectral approximations, Math. Computation 68, pp. 217-248, 1999 .
A. Guessab, A fast algorithm to compute Gaussian type quadrature formulae for spline functions, accepted for publication in Math. Computation (1999).
Q.I. Rahman, A. Guessab, Quadrature formulae and polynomial inequalities, J. Approx. Theory, 182, pp. 255-282, 1997.
Gout, J.-L.; Guessab, A. Sur les formules de quadrature numérique à nombre minimal de n\oe uds d'intégration. (French) [Cubature formulas with a minimal number of knots] Numer. Math. 49 (1986), no. 4, 439--455.
Gout, J.-L.; Guessab, A. Exemples de formules de quadrature numérique
à nombre minimal de n\oe uds sur des domaines à double symétrie
axiale. (French) [Examples of numerical quadrature formulas with a minimal number
of nodes on domains with double axial symmetry] RAIRO Modél. Math. Anal.
Numér. 20 (1986), no. 2, 287--314.
Rational F.E.
Gout, J.-L. Rational Wachspress-type finite elements on regular hexagons. IMA J. Numer. Anal. 5 (1985), no. 1, 59--77.
Apprato, D.; Arcangéli, R.; Gout, J. L. Sur les éléments finis rationnels de Wachspress. (French) Numer. Math. 32 (1979), no. 3, 247--270.
Apprato, D.; Arcangéli, R.; Gout, J. L. Rational interpolation of Wachspress error estimates. Comput. Math. Appl. 5 (1979), no. 4, 329--336.
Mathematical imaging :Level Set Methods - Geodesic Active Contours - Snakes
C. Gout, C. Le Guyader, L. Vese, Segmentation under geometrical conditions using geodesic active contours and interpolation using level set methods , Numerical Algorithms 39 (1-3), pp. 155–173, 2005.
D. Apprato, C. Gout, C. Le Guyader, The Level Set Methods and Image segmentation under interpolation conditions, Numerical Algorithms 39 (1-3), pp. 221–235, 2005.
D. Apprato, D. Ducassou, C. Gout, E. Laffon, C. Le Guyader, Segmentation of medical image sequence under constraints: application to non-invasive assessment of pulmonary arterial hypertension, Int. J. of Comp. Mathematics 5, pp. 527 - 536, 2004.
C. Gout, S. Vieira-Testé: An algorithm for segmentation under interpolation conditions using deformable models, Int. J. of Comp. Math., 80, no. 1, pp. 47-54, 2003.
Spline - Surface approximation
D. Apprato, C. Gout, C. Rabut, L. Traversoni, Multivariate approximation: An overview, Numerical Algorithms 39:, pp. 1–6, 2005.
Arcangéli, Rémi; López de Silanes, María Cruz; Torrens, Juan José. Multidimensional minimizing splines. Theory and applications. Grenoble Sciences. Kluwer Academic Publishers, Boston, MA, 2004. xvi+261 pp. ISBN: 1-4020-7786-6
D. Apprato, C. Gout, A result about scale transformation families in approximation: application to surface fitting from rapidly varying data, Numerical Algorithms 23 (2,3), pp. 263-279, 2000.
D. Apprato, C. Gout, D. Komatitsch, A New Method for $C^k$ Surface Approximation From a Set of Curves, With application to the Ship Track Data in the Marianas Trench, Mathematical Geology 34 (7), pp. 831-843, 2002.
D. Apprato, C. Gout, P. Sénéchal, Ck reconstruction of surfaces from partial data, Mathematical Geology 32 (8), pp. 969-983, 2000.
D. Apprato, C. Gout, Approximation de surfaces à partir de morceaux de surfaces, C. R. Acad. Sci. Paris, t. 325, SérieI , pp.445-448, 1997.
C. Gout,: C^k surface reconstruction from surface patches. In press, Computers & Mathematics with Applications, 44 (2002), no. 3-4, 389--406.
Arcangéli, R.; Rabut, C. Sur l'erreur d'interpolation par fonctions splines. (French) [Spline interpolation errors] RAIRO Modél. Math. Anal. Numér. 20 (1986), no. 2, 191--201.
Apprato, D.; Arcangéli, R.; Manzanilla, R. Sur la construction de surfaces de classe $C\sp k$ à partir d'un grand nombre de données de Lagrange. (French) [On the construction of $C\sp k$-surfaces starting from a large number of Lagrange data] RAIRO Modél. Math. Anal. Numér. 21 (1987), no. 4, 529--555.
Arcangéli, R. Some applications of discrete $D\sp m$ splines. Mathematical methods in computer aided geometric design (Oslo, 1988), 35--44, Academic Press, Boston, MA, 1989.
López de Silanes, M. C.; Arcangéli, R. Estimations de l'erreur d'approximation par splines d'interpolation et d'ajustement d'ordre $(m,s)$. (French) [Approximation error estimates for interpolating and smoothing $(m,s)$-splines] Numer. Math. 56 (1989), no. 5, 449--467
Torrens, J. J.; Serón, F. J.; López de Silanes, M. C.; Arcangéli, R.; Apprato, D. Finite-element interpolation of nonregular parametric surfaces. (Spanish) Contributions to the computation of curves and surfaces (Puerto de la Cruz, 1989), 101--108, Monogr. Acad. Ci. Exact. Fís.-Quím. Nat. Zaragoza, 2, Acad. Cienc. Exact. Fís. Quím. Nat. Zaragoza, Zaragoza, 1990.
López de Silanes, M. C.; Arcangéli, R. Sur la convergence des $D\sp m$-splines d'ajustement pour des données exactes ou bruitées. (French) [On the convergence of fitting $D\sp m$-splines for exact or noisy data] Rev. Mat. Univ. Complut. Madrid 4 (1991), no. 2-3, 279--294.
Apprato, D.; Arcangéli, R. Ajustement spline le long d'un ensemble de courbes. (French) [Spline fitting along a set of curves] RAIRO Modél. Math. Anal. Numér. 25 (1991), no. 2, 193--212.
Arcangéli, Rémi; Ycart, Bernard. Almost sure convergence of smoothing $D\sp m$-splines for noisy data. Numer. Math. 66 (1993), no. 3, 281--294.
Arcangéli, R.; Manzanilla, R.; Torrens, J. J. Approximation spline de surfaces de type explicite comportant des failles. (French) [Spline approximation of surfaces of explicit type which have faults] RAIRO Modél. Math. Anal. Numér. 31 (1997), no. 5, 643--676.