Université de Pau
UMR-CNRS 5142 Labo. de Mathématiques et leurs Applications de Pau
64000 Pau, France
APPROXIMATION PAPERS (University of Pau, France) - since 1974
Université de Pau
UMR-CNRS 5142 Labo. de Mathématiques
et leurs Applications de Pau
64000 Pau, France
Below, you will find several research activities (articles) from Pau school in:
Rational Finite Elements (since 1978...)
Mathematical imaging: Level Set Methods - Geodesic Active Contours - Snakes (since 2003...)
Approximation - Multivariate polynomial interpolation - Spline - Data approximation - Quadrature formulae - Numerica analysis (Since 1974...)
Rational F.E. - Wachspress F.E. (since 1978!...)
Gout, C., Apprato, D., Gout, J. L., Khayretdinova G., Wachspress Rational Finite Elements: $H^s$ Approximation Theory, Comparison with Generalized Barycentric Coordinates, and the VEM Connection, 62p., under review, 2026.
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.
Apprato, D.; Arcangéli, R. Approximation d’un problème aux limites elliptique d’ordre deux par éléments finis rationnels de Wachspress avec intégration numérique, M2AN 13, no 1 (1979), p. 3-20.
Gout J.L., Eléments finis polygonaux de Wachspress (PDF) (in French), University of Pau, 1980.
Apprato, D., Contribution à l'interpolation rationnelle de Wachspress (in French), University of Pau, 1978.
| Gout, J.L., |
Eléments finis polygonaux de Wachspress (PDF) (in French), University of Pau, 1980. Jury : P.G. Ciarlet, E.L. Wachspress, C. Coatmelec, J. Genet, M. Atteia, R. Arcangéli (Adv.) |
Etude de l'erreur d'interpolation d'Hermite dans IR^n. Eléments finis rationnels de type Wachspress sur un quadrilatère. Eléments finis rationnels pentagonaux et hexagonaux de type Wachspress. Estimation de l'erreur d'interpolation concernant les éléments finis droits polynomiaux et rationnels. Effet de l'intégration numérique dans la résolution d'un problème d'ordre 2 par éléments finis rationnels. Study of the Hermite interpolation error in IR^n. Rational finite elements of the Wachspress type on a quadrilateral. Pentagon- and hexagon-shaped rational finite elements of the Wachspress type. Estimation of the interpolation error for polynomial and rational straight-sided finite elements. Effect of numerical integration on the solution of a second-order problem using rational finite elements. |
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| Apprato, D., | Contribution à l'interpolation rationnelle de Wachspress (in French), University of Pau, 1978. |
Ce travail est consacré à une étude d'éléments finis rationnels droits et courbes de Lagrange dans IR^2 suivant l'approche faite par Wachspress dans son livre. Dans la perspective d'une éventuelle utilisation de ces éléments finis, on s'est limité à certains d'entre eux. On a donc principalement étudié les éléments finis rationnels droits construits sur un quadrilatère, avec l'erreur d'interpolation correspondante et leur utilisation dans des problèmes avec intégration numérique. En ce qui concerne les éléments finis rationnels courbes on s'est borné à donner la construction de deux d'entre eux, l'estimation de l'erreur présentant das ce cas des difficultés non toujours résolues... This work is devoted to the study of straight and curved rational Lagrange finite elements in IR^2, following the approach proposed by Wachspress' book. With a view toward the possible use of such finite elements, the study was restricted to certain specific types. We have therefore mainly focused on straight rational finite elements defined over a quadrilateral, analyzing the corresponding interpolation error and their application to problems involving numerical integration. As for curved rational finite elements, we have limited ourselves to constructing two examples, since estimating the interpolation error in this case presents difficulties that are not yet fully resolved. |
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Mathematical imaging: Level Set Methods - Geodesic Active Contours - Snakes (since 2003...)
G. Khayretdinova, D. Apprato, C. Gout, A level set based model for image
segmentation under geometric constraints and data approximation, Journal of
Imaging 10-1 (2), 19p., 2024.
G. Khayretdinova, T. Chaumont-Frelet, C. Gout, S. Kuksenko,
Image segmentation with a priori conditions: applications to medical and geophysical
imaging, Math. Comput. Appl. 27(2), 26, 2022.
S. Ozeré, C. Le Guyader, C. Gout, Joint segmentation/registration
model by shape alignment via weighted total variation minimization and nonlinear
elasticity, SIAM J. on Imaging Sciences 8(3), 1981-2020, 2015.
R. Derfoul, S. Da Veiga, C. Gout, C. Le Guyader, E. Tillier, Image processing
tools for better incorporation of 4D seismic data, into reservoir models, J.
of Comp. and Applied Math. 240, pp. 111-122, 2013.
C. Le Guyader, C. Gout, A.S. Macé, D. Apprato. Gradient fields
approximation: application to registration processes in image processing, J.
of Comp. and Applied Math. 240, pp. 135-147, 2013.
C. Le Guyader, D. Apprato, C. Gout, On the Construction
of Topology-Preserving Deformation Fields, IEEE Transactions on Image Processing
21 (4) , art. No. 6093964 , pp. 1587-1599, 2012
C. Gout, C. Le Guyader, L. Romani, A.G. Saint-Guirons, Approximation of surfaces with fault(s) and/or rapidly varying data, using a segmentation process, $D^m$-splines and the finite element method, Num. Algo. 48 (1), p. 67-92, 2008.
C. Le Guyader, C. Gout, Geodesic active contour under geometrical conditions: Theory and 3D Applications, Num. Algo. 48 (2), p. 105-134, 2008.
N. Forcadel, C. Le Guyader, C. Gout, Image segmentation
using a Generalized Fast Marching Method, Numerical Algorithms, Num. Algo. 48
(2), p. 189-212, 2008.
C. Gout, Viscosity solutions for Geodesic Active contour
under interpolation conditions, I.J. Comp. Math., no. 9, 1375-1395, 2008.
C. Gout, C; Guyader, Segmentation of complex geophysical
structures with well data, Comput. Geosci. Vol. 10, no. 4, pp. 361-372, 2006.
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.
Approximation - Multivariate polynomial interpolation - Spline - Data approximation - Numerica analysis (Since 1974...)
F Dell’Accio, A Guessab, M Kbiri Alaoui, F Nudo, A general probability density framework for local histopolation and weighted function reconstruction from mesh line integrals, Numerical Algorithms, 1-43, 2026.
A. Leclerc, H. Barucq, M. Duruflé, C. Gout, A. Tonnoir, Modal computation for an open Helmholtz eigenvalue problem, en cours de modifications, Computers and Mathematics with Applications, 211, pp.59-75, 2026.
F Dell’Accio, A Guessab, GV Milovanovi, F Nudo, Reconstructing algebraic functions from a nonconforming exponential weighted enriched finite element, Journal of Computational and Applied Mathematics 466, 2025.
F Dell’Accio, A Guessab, GV Milovanovi, F Nudo, Truncated Neugebauer-Hermite weighted approach for the enrichment of the Crouzeix-Raviart finite element, BIT Numerical Mathematics 65 (2), 24, 2025.
F Dell’Accio, A Guessab, F Nudo, Improved methods for the enrichment and analysis of the simplicial vector-valued linear finite elements, Mathematics and Computers in Simulation 230, 370-385, 2025.
F Dell’Accio, A Guessab, F Nudo, New quadratic and cubic polynomial enrichments of the Crouzeix–Raviart finite element, Computers & Mathematics with Applications 170, 204-212, 2024.
F Dell’Accio, F Di Tommaso, A Guessab, F Nudo, A general class of enriched methods for the simplicial linear finite elements, Applied Mathematics and Computation 456, 2023.
F Dell’Accio, F Di Tommaso, A Guessab, F Nudo, Enrichment strategies for the simplicial linear finite elements, Applied Mathematics and Computation 451, 2023.
F Nudo, F Dell’Accio, F Di Tommaso, A Guessab, A general strategy for enriching simplicial linear finite elements, Numerical Computations: Theory and Algorithms NUMTA, 2023.
F Dell’Accio, F Di Tommaso, A Guessab, F Nudo, A unified enrichment approach of the standard three-node triangular element, Applied Numerical Mathematics 187, 1-23, 2023.
F Dell’Accio, F Di Tommaso, A Guessab, F Nudo, On the improvement of the triangular Shepard method by non conformal polynomial elements, Applied Numerical Mathematics 184, 446-460, 2023.
F Dell’Accio, F Di Tommaso, A Guessab, F Nudo, A general class of enriched methods for the simplicial linear finite elements, Applied Mathematics and Computation 456 (C), 2023.
F Dell’Accio, F Di Tommaso, A Guessab, F Nudo, Enrichment strategies for the simplicial linear finite elements, Applied Mathematics and Computation 451, 2023.
A Guessab, A Characterization for the Validity of the Hermite–Hadamard Inequality on a Simplex, Approximation and Computation in Science and Engineering, 369-396, 2022.
O Alabdali, A Guessab, Optimal estimates of approximation errors for strongly positive linear operators on convex polytopes, Filomat 36 (2), 695-701, 2022.
A Guessab, Sharp Approximations Base on Delaunay Triangulations and Voronoi Diagrams, Novosibirsk: NSU Publishing and Printing Center, 2022.
A Guessab, B Semisalov, Optimal general Hermite-Hadamard-type inequalities in a ball and their applications in multidimensional numerical integration, Applied Numerical Mathematics 170, 83-108, 2022.
G Allal, D Abderrazak, N Otheman, A Guessab, A Driouch, A globally convergent modified version of the method of moving asymptotes (vol 13, pg 905, 2019), Applicable Analysis and Discrete Mathematics 15 (2), 518-518, 2021.
A Guessab, A Driouch, A globally convergent modified multivariate version of the method of moving asymptotes, Applicable Analysis and Discrete Mathematics 15 (2), 519-535, 2021.
A Guessab, Y Simsek, Recent Advances in General Inequalities on Pure & Applied Mathematics and Related Areas-An Issue Dedicated to GV Milovanovi?, Journal of Inequalities and Applications, 2021.
A Guessab, A Driouch, Correction to: A globally convergent modified version of the method of moving asymptotes, Applicable Analysis and Discrete Mathematics 15 (518), 518, 2021.
M.-P. Schmidt, L. Couret, C. B.W. Pedersen, C. Gout, Structural Topology Optimization with Anisotropic Materials for Continuous Fiber Designs, Structural and Multidisciplinary Optimization 62, pp. 3105-3126, 2020.
A Guessab, A Driouch, O Nouisser, A globally convergent modified version of the method of moving asymptotes, Applicable Analysis and Discrete Mathematics 14 (3), 614-626, 2020.
A Guessab, TA Roushan, Generalized Barycentric Coordinates and Sharp Strongly Negative Definite Multidimensional Numerical Integration, Approximation Theory and Analytic Inequalities, 179-199, 2020.
O Alabdali, A Guessab, Multidimensional Numerical Integration Under Strong Convexity, Filomat 34 (2), 2020.
O Alabdali, A Guessab, Sharp multidimensional numerical integration for strongly convex functions on convex polytopes, Filomat 34 (2), 601-607, 2020.
H. Calandra, Z. Lambert, C. Gout, A. Atle, M. Bonnasse-Gahot, J. Diaz, S. Ettouati, Recent advances in numerical methods for solving the wave equation in the context of seismic depth imaging, SMAI J. of Computational Mathematics, Volume 5S, p. 47-65, 2019.
P. Gonzalez Casanova, C. Gout, J. Zavaleta, Radial basis function methods for optimal control of the convection-diffusion equation: A numerical study, Eng. Analysis with Boundary Elements 108, pp. 101-109, 2019.
N. Warncke, I. Ciotir, A. Tonnoir, C. Gout and Z. Lambert, Analytical approach to Galerkin BEMs on polyhedral surfaces, SMAI J. of Computational Mathematics, Volume 5S, p. 27-46, 2019.
M.-P. Schmidt, C. B.W. Pedersen, C. Gout, On structural topology optimization using graded porosity control, Structural and Multidisciplinary Optimization (60 - 4), pp. 1437--1453, 2019.
A Guessab, GV Milovanovi?, Best Constants for Poincaré–Type Inequalities in, Differential and Integral Inequalities, 391-402, 2019.
B Achchab, A Agouzal, A Guessab, Y Zaim, An extended family of nonconforming quasi-Wilson elements for solving elasticity problem, Applied Mathematics and Computation 344, 1-19, 2019.
MW Alomari, A Guessab, Lp–error bounds of two and three–point quadrature rules for Riemann–Stieltjes integrals, Moroccan journal of pure and applied analysis 4 (1), 33-43, 2019.
A Guessab, B Semisalov, Extended multidimensional integration formulas on polytope meshes, SIAM Journal on Scientific Computing 41 (5), A3152-A3181, 2019.
O Alabdali, A Guessab, G Schmeisser, Characterizations of uniform convexity for differentiable functions, Applicable Analysis and Discrete Mathematics 13 (3), 721-732, 2019.
D. Cervantes, P. Gonzalez, C. Gout, M. Moreles, A line search algorithm for wind field adjustment with incomplete data and RBF approximation, Comp. and Applied Math., Volume 37, Issue 3, pp 2519-2532, 2018.
A Guessab, B Semisalov, Numerical integration using integrals over hyperplane sections of simplices in a triangulation of a polytope, BIT Numerical Mathematics 58 (3), 613-660, 2018.
A Guessab, B Semisalov, A multivariate version of Hammer’s inequality and its consequences in numerical integration, Results in Mathematics 73 (1), 33, 2018.
H. Barucq, T. Chaumont Frelet, C. Gout, Stability analysis of heterogeous Helmholtz problems and finite element solution based on propagation media approximation, Math. of Computation, Volume 86, Number 307, Pages 2129-2157, 2017.
M Bachar, A Guessab, O Mohammed, Y Zaim, New cubature formulas and Hermite–Hadamard type inequalities using integrals over some hyperplanes in the d-dimensional hyper-rectangle, Applied Mathematics and Computation 315, 347-362, 2017.
A Guessab, Y Zaim, A unified and general framework for enriching finite element approximations, Progress in Approximation Theory and Applicable Complex Analysis, 2017.
M Bachar, A Guessab, Characterization of the existence of an enriched linear finite element approximation using biorthogonal systems, Results in Mathematics 70 (3), 401-413, 2016.
M Bachar, A Guessab, A simple necessary and sufficient condition for the enrichment of the Crouzeix-Raviart element, Applicable Analysis and Discrete Mathematics 10 (2), 378-393, 2016.
A Guessab, Generalized barycentric coordinates and Jensen type inequalities on convex polytopes, HAL (Le Centre pour la Communication Scientifique Directe), 2016.
A Guessab, On the Enrichment of finite-element approximations, International Conference Mathematical and Computational Methods, 2016.
B Achchab, A Guessab, Y Zaim, A new class of nonconforming finite elements for the enrichment of Q1 element on convex polytope, Applied Mathematics and Computation 271, 657-668, 2015.
B Achchab, K Bouihat, A Guessab, G Schmeisser, A general approach to the construction of nonconforming finite elements on convex polytopes, Applied Mathematics and Computation 268, 916-923, 2015.
D. Apprato, C. Gout, C. Le Guyader, Spline approximation of gradient fields: applications to wind velocity fields, Mathematics and Computers in Simulation 97, pp. 260-279, 2014.
H Alzer, A Guessab, An integral inequality for cosine polynomials, Applied Mathematics and Computation 249, 532-534, 2014.
OYM Alabdali, A Guessab, On the approximation of strongly convex functions by an upper or lower operator, Applied Mathematics and Computation 247, 1129-1138, 2014.
B Achchab, A Guessab, On approximation of linear functionals over convex functions: Construction techniques and new directions, Applied Mathematics and Computation 247, 417-430, 2014.
A Guessab, Symmetrization procedures and convexity in centrally symmetric polytopes, Applied Mathematics and Computation 243, 74-82, 2014.
A Guessab, Approximations of differentiable convex functions on arbitrary convex polytopes, Applied Mathematics and Computation 240, 326-338, 2014.
A Guessab, F Guessab, Symmetrization, convexity and applications, Applied Mathematics and Computation 240, 149-160, 2014.
M Bachar, T Estebenet, A Guessab, A moving asymptotes algorithm using new local convex approximation methods with explicit solutions, Electronic Transactions on Numerical Analysis 43, 21-44, 2014.
A Guessab, Diagrammes de Voronoi, triangulations de Delaunay et optimisation de maillage basée sur une analyse de l'erreur locale d'interpolation, Méthodes numériques pour les problèmes de pollution des eaux, 2014.
C. Gout, L. Romani, Multivariate Approximation: Theory and applications, Journal of Computational and Applied Mathematics 240, pp. 1-4, 2013.
D. Cervantes, P. Gonzalez, C. Gout, R. Resendiz, H. Juarez, Vector field approximation using radial basis functions, J. of Comp. and Applied Math. 240 , pp. 163-173, 2013.
A Guessab, Formules de quadrature dans R² avec réseau, Numerical Integration IV, 2013.
D Barrera, A Guessab, MJ Ibáñez, O Nouisser, Increasing the approximation order of spline quasi-interpolants, Journal of computational and applied mathematics 252, 27-39, 2013.
A Guessab, Generalized barycentric coordinates and approximations of convex functions on arbitrary convex polytopes, Computers & Mathematics with Applications 66 (6), 1120-1136, 2013.
A Guessab, G Schmeisser, Necessary and sufficient conditions for the validity of Jensen’s inequality, Archiv der Mathematik 100 (6), 561-570, 2013.
D Barrera, A Guessab, MJ Ibáñez, O Nouisser, Construction techniques for multivariate modified quasi-interpolants with high approximation order, Computers & Mathematics with Applications 65 (1), 29-41, 2013.
A Guessab, Lower and upper bounds for positive linear functionals, Journal of Nonlinear and Convex Analysis, 2013.
A Guessab, M Moncayo, G Schmeisser, A class of nonlinear four-point subdivision schemes: Properties in terms of conditions, Advances in Computational Mathematics 37 (2), 151-190, 2012.
A Guessab, O Nouisser, J Pecaric, A multivariate extension of an inequality of Brenner–Alzer, Archiv der Mathematik 98 (3), 277-287, 2012.
A Guessab, Direct and converse results for generalized multivariate Jensen-type inequalities, J. Nonlinear Convex Anal 13 (4), 777-797, 2012.
A Guessab, MJ Ibáñez, O Nouisser, Error analysis for a non-standard class of differential quasi-interpolants, Mathematics and Computers in Simulation 81 (10), 2190-2200, 2011.
D Barrera, A Guessab, MJ Ibáñez, O Nouisser, Optimal bivariate C1 cubic quasi-interpolation on a type-2 triangulation, Journal of computational and applied mathematics 234 (4), 1188-1199, 2010.
A Guessab, G Schmeisser, Negative definite cubature formulae, extremality and Delaunay triangulation, Constructive Approximation 31 (1), 95-113, 2010.
A Guessab, G Schmeisser, Construction of positive definite cubature formulae and approximation of functions via Voronoi tessellations, Advances in Computational Mathematics 32 (1), 25, 2010.
A Guessab, O Nouisser, G Schmeisser, Enhancement of the algebraic precision of a linear operator and consequences under positivity, Positivity 13 (4), 693-707, 2009.
C. de Boor, C. Gout, A. Kunoth, C. Rabut, Multivariate Approximation: An overview, Num. Algo. 48 (1), p. 1-10, 2008.
C. Gout, C. Le Guyader, L. Romani, A.G. Saint-Guirons, Approximation of surfaces with fault(s) and/or rapidly varying data, using a segmentation process, $D^m$-splines and the finite element method, Num. Algo. 48 (1), p. 67-92, 2008.
A Guessab, G Schmeisser, Two Korovkin-type theorems in multivariate approximation, Banach Journal of Mathematical Analysis 2 (2), 121-128, 2008.
A Guessab, O Nouisser, G Schmeisser, A definiteness theory for cubature formulae of order two, Constructive approximation 24 (3), 263-288, 2006.
A Guessab, O Nouisser, G Schmeisser, Multivariate approximation by a combination of modified Taylor polynomials, Journal of Computational and Applied Mathematics 196 (1), 162-179, 2006.
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.
D. Apprato, C. Gout, D. Komatitsch, A New Method for $C^k$ Surface Approximation From a Set of Curves, Mathematical Geology 34 (7), pp. 831-843, 2002.
C. Gout, $C^k$ surface reconstruction from surface patches, Computers & Mathematics with Applications, 44 (3-4), 389--406, 2002.
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, P. Sénéchal, Ck reconstruction of surfaces from partial data, Mathematical Geology 32 (8), pp. 969-983, 2000.
Arcangéli, R.; Manzanilla, R.; Torrens, J. J., Approximation spline de surfaces de type explicite comportant des failles, RAIRO Modél. Math. Anal. Numér. 31 (5), 643--676, 1997.
D. Apprato, C. Gout, Approximation de surfaces à partir de morceaux de surfaces, C. R. Acad. Sci. Paris, t. 325, Série I, pp. 445-448, 1997.
Arcangéli, Rémi; Ycart, Bernard, Almost sure convergence of smoothing $D^m$-splines for noisy data, Numer. Math. 66 (3), 281--294, 1993.
López de Silanes, M. C.; Arcangéli, R., Sur la convergence des $D^m$-splines d'ajustement pour des données exactes ou bruitées, Rev. Mat. Univ. Complut. Madrid 4 (2-3), 279--294, 1991.
Apprato, D.; Arcangéli, R., Ajustement spline le long d'un ensemble de courbes, RAIRO Modél. Math. Anal. Numér. 25 (2), 193--212, 1991.
Torrens, J. J.; Serón, F. J.; López de Silanes, M. C.; Arcangéli, R.; Apprato, D., Finite-element interpolation of nonregular parametric surfaces, Monogr. Acad. Ci. Exact. Fís.-Quím. Nat. Zaragoza, 2, 101--108, 1990.
Arcangéli, R., Some applications of discrete $D^m$ splines, Mathematical methods in computer aided geometric design, 35--44, Academic Press, 1989.
López de Silanes, M. C.; Arcangéli, R., Estimations de l'erreur d'approximation par splines d'interpolation et d'ajustement d'ordre $(m,s)$, Numer. Math. 56 (5), 449--467, 1989.
Apprato, D.; Arcangéli, R.; Manzanilla, R., Sur la construction de surfaces de classe $C^k$ à partir d'un grand nombre de données de Lagrange, RAIRO Modél. Math. Anal. Numér. 21 (4), 529--555, 1987.
Arcangéli, R.; Rabut, C., Sur l'erreur d'interpolation par fonctions splines, RAIRO Modél. Math. Anal. Numér. 20 (2), 191--201, 1986.
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
Arcangeli, R.; Gout, J. L., Sur l'évaluation de l'erreur d'interpolation de Lagrange dans un ouvert de $\mathbb{R}^n$. Revue française d'automatique, informatique, recherche opérationnelle. Analyse numérique, 10 no. 1 (1976), p. 5-27
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.
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