On Lattices Admitting Unique Lagrange Interpolations

Previous article Next article On Lattices Admitting Unique Lagrange InterpolationsK. C. Chung and T. H. YaoK. C. Chung and T. H. Yaohttps: //doi. org/10. 1137/0714050PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractIn this paper generalizations of the classical Lagrange interpolation formula to n-dimensional spaces are discussed. It simplifies and improves upon certain results of some recent authors. 1 P. G. Ciarlet and, P. -A. Raviart, General Lagrange and Hermite interpolation in Rn with applications to finite element methods, Arch. Rational Mech. Anal. , 46 (1972), 177–199 10. 1007/BF00252458 MR0336957 0243. 41004 CrossrefISIGoogle Scholar2 P. G. Ciarlet and, C. Wagschal, Multipoint Taylor formulas and applications to the finite element method, Numer. Math. , 17 (1971), 84–100 10. 1007/BF01395869 MR0287666 0199. 50104 CrossrefISIGoogle Scholar3 Christian Coatmélec, Approximation et interpolation des fonctions différentiables de plusieurs variables, Ann. Sci. École Norm. Sup. (3), 83 (1966), 271–341 MR0232143 0155. 10902 CrossrefGoogle Scholar4 R. A. Nicolaides, On a class of finite elements generated by Lagrange interpolation, SIAM J. Numer. Anal. , 9 (1972), 435–445 10. 1137/0709039 MR0317511 0282. 65009 LinkISIGoogle Scholar5 Miloš Zlámal, On the finite element method, Numer. Math. , 12 (1968), 394–409 MR0243753 0176. 16001 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Unisolvency for Polynomial Interpolation in Simplices with Symmetrical Nodal DistributionsJournal of Scientific Computing, Vol. 92, No. 2 | 2 July 2022 Cross Ref A new proof of the Gasca - Maeztu conjecture for n = 5Proceedings of NAS RA. Mathematics | 18 July 2022 Cross Ref The Discrete Approximation Problem for a Special Case of Hermite-Type Polynomial InterpolationJournal of Systems Science and Complexity, Vol. 6 | 20 June 2022 Cross Ref Combining interpolation schemes and Lagrange interpolation on the unit sphere in ℝN+1Ukrains'kyi Matematychnyi Zhurnal, Vol. 74, No. 4 | 23 May 2022 Cross Ref A New Proof of the Gasca–Maeztu Conjecture for n=5Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), Vol. 57, No. 3 | 22 June 2022 Cross Ref Solving Hermite Interpolation Problem in Finite-Dimensional Euclidean SpaceCybernetics and Systems Analysis, Vol. 58, No. 2 | 23 June 2022 Cross Ref Padua points and fake nodes for polynomial approximation: old, new and open problemsConstructive Mathematical Analysis, Vol. 5, No. 1 | 1 March 2022 Cross Ref Taylor type and Hermite type interpolants in R^nNumerical Algorithms, Vol. 89, No. 1 | 26 April 2021 Cross Ref On a generalization of the Lebesgue's constantJournal of Computational Physics, Vol. 428 | 1 Mar 2021 Cross Ref On the basic properties of GCn setsJournal of Knot Theory and Its Ramifications, Vol. 29, No. 14 | 20 January 2021 Cross Ref Radon's construction and matrix relations generating syzygiesMonatshefte für Mathematik, Vol. 192, No. 2 | 12 February 2020 Cross Ref On the usage of lines in GCn setsAdvances in Computational Mathematics, Vol. 45, No. 5-6 | 3 June 2019 Cross Ref Stable Controller Design for T–S Fuzzy Control Systems with Piecewise Multi-linear Interpolations into Membership FunctionsInternational Journal of Fuzzy Systems, Vol. 21, No. 5 | 12 June 2019 Cross Ref Extensions of planar GC sets and syzygy matricesAdvances in Computational Mathematics, Vol. 45, No. 2 | 13 September 2018 Cross Ref On a correction of a property of GCn setsAdvances in Computational Mathematics, Vol. 45, No. 1 | 12 June 2018 Cross Ref Model reduction of parabolic PDEs using multivariate splinesInternational Journal of Control, Vol. 92, No. 1 | 21 September 2016 Cross Ref Polynomial Chaos and Collocation Methods and Their Range of ApplicabilityUncertainty Management for Robust Industrial Design in Aeronautics | 21 July 2018 Cross Ref Observations on Interpolation by Total Degree Polynomials in Two VariablesConstructive Approximation, Vol. 47, No. 3 | 30 May 2017 Cross Ref Lagrange-type basis for multivariate uniform integrable tensor-product Birkhoff interpolationMathematical Methods in the Applied Sciences, Vol. 40, No. 18 | 12 July 2017 Cross Ref On a new property of n-poised and G C n setsAdvances in Computational Mathematics, Vol. 43, No. 3 | 16 November 2016 Cross Ref High Order Mass-Lumping Finite Elements on SimplexesNumerical Mathematics: Theory, Methods and Applications, Vol. 10, No. 2 | 9 May 2017 Cross Ref Polynomial Interpolation in Higher Dimension: From Simplicial Complexes to GC SetsNathan Fieldsteel and Hal SchenckSIAM Journal on Numerical Analysis, Vol. 55, No. 1 | 19 January 2017AbstractPDF (441 KB) Interpolation with symmetric polynomialsNumerical Algorithms, Vol. 74, No. 1 | 26 April 2016 Cross Ref Quartic splines on Powell–Sabin triangulationsComputer Aided Geometric Design, Vol. 49 | 1 Dec 2016 Cross Ref Simplex-stochastic collocation method with improved scalabilityJournal of Computational Physics, Vol. 310 | 1 Apr 2016 Cross Ref Trivariate spline quasi-interpolants based on simplex splines and polar formsMathematics and Computers in Simulation, Vol. 118 | 1 Dec 2015 Cross Ref Stochastic Polynomial Interpolation for Uncertainty Quantification With Computer ExperimentsTechnometrics, Vol. 57, No. 4 | 18 November 2015 Cross Ref Superconvergent C¹ C 1 cubic spline quasi-interpolants on Powell-Sabin partitionsBIT Numerical Mathematics, Vol. 55, No. 3 | 12 September 2014 Cross Ref On Configurations of Points on the Sphere and Applications to Approximation of Holomorphic Functions by Lagrange InterpolantsComputational Methods and Function Theory, Vol. 15, No. 3 | 29 January 2015 Cross Ref A Family of Smooth Quasi-interpolants Defined Over Powell–Sabin TriangulationsConstructive Approximation, Vol. 41, No. 2 | 26 July 2014 Cross Ref Superconvergent trivariate quadratic spline quasi-interpolants on Worsey–Piper splitJournal of Computational and Applied Mathematics, Vol. 276 | 1 Mar 2015 Cross Ref Superconvergent local quasi-interpolants based on special multivariate quadratic spline space over a refined quadrangulationApplied Mathematics and Computation, Vol. 250 | 1 Jan 2015 Cross Ref Superconvergent quadratic spline quasi-interpolants on Powell–Sabin partitionsApplied Numerical Mathematics, Vol. 87 | 1 Jan 2015 Cross Ref Cubic spline quasi-interpolants on Powell–Sabin partitionsBIT Numerical Mathematics, Vol. 54, No. 4 | 15 April 2014 Cross Ref The Gasca–Maeztu conjecture for n=5 n = 5Numerische Mathematik, Vol. 127, No. 4 | 21 November 2013 Cross Ref A normalized basis for cubic super spline space on Powell–Sabin triangulationMathematics and Computers in Simulation, Vol. 99 | 1 May 2014 Cross Ref Interpolation and MonotonicityPotential Theory | 11 April 2014 Cross Ref Low depth quantum circuits for Ising modelsAnnals of Physics, Vol. 340, No. 1 | 1 Jan 2014 Cross Ref Construction of quintic Powell–Sabin spline quasi-interpolants based on blossomingJournal of Computational and Applied Mathematics, Vol. 250 | 1 Oct 2013 Cross Ref Local quasi-interpolants based on special multivariate quadratic spline space over a refined quadrangulationApplied Mathematics and Computation, Vol. 219, No. 21 | 1 Jul 2013 Cross Ref On the continuity of multivariate Lagrange interpolation at natural latticesLMS Journal of Computation and Mathematics, Vol. 16 | 10 April 2013 Cross Ref Probabilistic Collocation Method in Solving Eulerian Model for Air Traffic Flow Managementemail protected 2012 | 6 September 2012 Cross Ref Generalizations of known constructions of correct knotsJournal of Contemporary Mathematical Analysis, Vol. 47, No. 2 | 24 April 2012 Cross Ref Normalized trivariate B-splines on Worsey-Piper split and quasi-interpolantsBIT Numerical Mathematics, Vol. 52, No. 1 | 31 August 2011 Cross Ref Polynomials and identities on real Banach spacesJournal of Mathematical Analysis and Applications, Vol. 385, No. 2 | 1 Jan 2012 Cross Ref On Radon's recipe for choosing correct sites for multivariate polynomial interpolationJournal of Approximation Theory, Vol. 163, No. 12 | 1 Dec 2011 Cross Ref High-order, multidimensional, and conservative coarse–fine interpolation for adaptive mesh refinementComputer Methods in Applied Mechanics and Engineering, Vol. 200, No. 45-46 | 1 Oct 2011 Cross Ref Interpolation and convergence of Bernstein-Bézier coefficientsActa Mathematica Sinica, English Series, Vol. 27, No. 9 | 15 August 2011 Cross Ref Unisolvency for multivariate polynomial interpolation in Coatmèlec configurations of nodesApplied Mathematics and Computation, Vol. 217, No. 18 | 1 May 2011 Cross Ref Conjectures on GCn setsJournal of Contemporary Mathematical Analysis, Vol. 46, No. 2 | 1 May 2011 Cross Ref Lattices on simplicial partitions which are not simply connectedJournal of Computational and Applied Mathematics, Vol. 235, No. 1 | 1 Nov 2010 Cross Ref The properly posed set of nodes of multivariate Lagrange interpolation along algebraic manifoldApplicable Analysis, Vol. 89, No. 3 | 1 Mar 2010 Cross Ref Lattices on simplicial partitionsJournal of Computational and Applied Mathematics, Vol. 233, No. 7 | 1 Feb 2010 Cross Ref Configurations of nodes with defects greater than threeJournal of Computational and Applied Mathematics, Vol. 233, No. 7 | 1 Feb 2010 Cross Ref Multivariate polynomial interpolation: Aitken–Neville sets and generalized principal latticesJournal of Approximation Theory, Vol. 161, No. 1 | 1 Nov 2009 Cross Ref Superposition interpolation process inApplied Mathematics and Computation, Vol. 215, No. 1 | 1 Sep 2009 Cross Ref Newton–Cotes cubature rules over (d+1) -pencil latticesJournal of Computational and Applied Mathematics, Vol. 231, No. 1 | 1 Sep 2009 Cross Ref A new proof of the Gasca–Maeztu conjecture for n=4Journal of Approximation Theory, Vol. 159, No. 2 | 1 Aug 2009 Cross Ref A new algorithm for a recursive construction of the minimal interpolation spaceMathematics and Computers in Simulation, Vol. 79, No. 12 | 1 Aug 2009 Cross Ref A generalized finite difference method using Coatmèlec latticesComputer Physics Communications, Vol. 180, No. 7 | 1 Jul 2009 Cross Ref Polar forms and quadratic spline quasi-interpolants on Powell–Sabin partitionsApplied Numerical Mathematics, Vol. 59, No. 5 | 1 May 2009 Cross Ref Multipartite Secret Sharing by Bivariate InterpolationJournal of Cryptology, Vol. 22, No. 2 | 30 July 2008 Cross Ref Fast and stable evaluation of box-splines via the BB-formNumerical Algorithms, Vol. 50, No. 4 | 2 September 2008 Cross Ref Classification of sets satisfying the geometric characterizationNumerical Algorithms, Vol. 50, No. 2 | 27 June 2008 Cross Ref Aitken–Neville sets, principal lattices and divided differencesJournal of Approximation Theory, Vol. 156, No. 2 | 1 Feb 2009 Cross Ref A local least-squares method for solving nonlinear partial differential equations of second orderNumerische Mathematik, Vol. 111, No. 3 | 20 November 2008 Cross Ref Lattices on tetrahedral partitionsANNALI DELL'UNIVERSITA' DI FERRARA, Vol. 54, No. 2 | 15 November 2008 Cross Ref Barycentric coordinates for Lagrange interpolation over lattices on a simplexNumerical Algorithms, Vol. 48, No. 1-3 | 20 February 2008 Cross Ref A recursive method for computing interpolantsJournal of Computational and Applied Mathematics, Vol. 216, No. 2 | 1 Jul 2008 Cross Ref An analysis of polynomial chaos approximations for modeling single-fluid-phase flow in porous medium systemsJournal of Computational Physics, Vol. 226, No. 2 | 1 Oct 2007 Cross Ref Multivariate polynomial interpolation: conjectures concerning GC-setsNumerical Algorithms, Vol. 45, No. 1-4 | 15 March 2007 Cross Ref Three-pencil lattices on triangulationsNumerical Algorithms, Vol. 45, No. 1-4 | 20 February 2007 Cross Ref Some researches on multivariate Lagrange interpolation along the sufficiently intersected algebraic manifoldApplicable Analysis, Vol. 86, No. 6 | 1 Jun 2007 Cross Ref Generalized principal lattices and cubic pencilsNumerical Algorithms, Vol. 44, No. 2 | 26 May 2007 Cross Ref Geometric characterization and generalized principal latticesJournal of Approximation Theory, Vol. 143, No. 1 | 1 Nov 2006 Cross Ref Interpolation lattices in several variablesNumerische Mathematik, Vol. 102, No. 4 | 25 January 2006 Cross Ref Multipartite Secret Sharing by Bivariate InterpolationAutomata, Languages and Programming | 1 Jan 2006 Cross Ref Interpolation on lattices generated by cubic pencilsAdvances in Computational Mathematics, Vol. 24, No. 1-4 | 1 Jan 2006 Cross Ref Polynomial Interpolation in Several Variables: Lattices, Differences, and IdealsTopics in Multivariate Approximation and Interpolation | 1 Jan 2006 Cross Ref Intertwining unisolvent arrays for multivariate Lagrange interpolationAdvances in Computational Mathematics, Vol. 23, No. 4 | 1 Nov 2005 Cross Ref Generation of lattices of points for bivariate interpolationNumerical Algorithms, Vol. 39, No. 1-3 | 1 Jul 2005 Cross Ref Trivariate spline approximations of 3D Navier-Stokes equationsMathematics of Computation, Vol. 74, No. 250 | 2 September 2004 Cross Ref High-Order Collocation Methods for Differential Equations with Random InputsDongbin Xiu and Jan S. HesthavenSIAM Journal on Scientific Computing, Vol. 27, No. 3 | 25 July 2006AbstractPDF (414 KB) Interpolation by ridge polynomials and its application in neural networksJournal of Computational and Applied Mathematics, Vol. 144, No. 1-2 | 1 Jul 2002 Cross Ref On a Hermite Interpolation by Polynomials of Two VariablesBorislav Bojanov and Yuan XuSIAM Journal on Numerical Analysis, Vol. 39, No. 5 | 26 July 2006AbstractPDF (196 KB) A note on bivariate Lagrange interpolation on algebraic curvesStudia Scientiarum Mathematicarum Hungarica, Vol. 38, No. 1-4 | 1 May 2001 Cross Ref Properly Posed Sets of Nodes for Multivariate Lagrange Interpolation in CsXue-Zhang Liang, Chun-Mei Lü, and Ren-Zhong FengSIAM Journal on Numerical Analysis, Vol. 39, No. 2 | 25 July 2006AbstractPDF (136 KB) Multivariate Hermite interpolation by algebraic polynomials: A surveyJournal of Computational and Applied Mathematics, Vol. 122, No. 1-2 | 1 Oct 2000 Cross Ref Stable Spectral Methods on Tetrahedral ElementsJ. S. Hesthaven and C. H. TengSIAM Journal on Scientific Computing, Vol. 21, No. 6 | 25 July 2006AbstractPDF (261 KB) Stable spectral methods for conservation laws on triangles with unstructured gridsComputer Methods in Applied Mechanics and Engineering, Vol. 175, No. 3-4 | 1 Jul 1999 Cross Ref A new approach to interpolating scaling functionsApplicable Analysis, Vol. 72, No. 3-4 | 1 Apr 1999 Cross Ref The Discrete Petrov-Galerkin Method for Weakly Singular Integral EquationsJournal of Integral Equations and Applications, Vol. 11, No. 1 | 1 Mar 1999 Cross Ref A Construction of Refinable Sets for Interpolating WaveletsResults in Mathematics, Vol. 34, No. 3-4 | 17 April 2013 Cross Ref Lattices and Algorithms for Bivariate Bernstein, Lagrange, Newton, and Other Related Polynomial Bases Based on Duality betweenL-Bases andB-BasesJournal of Approximation Theory, Vol. 93, No. 1 | 1 Apr 1998 Cross Ref From Electrostatics to Almost Optimal Nodal Sets for Polynomial Interpolation in a SimplexJ. S. HesthavenSIAM Journal on Numerical Analysis, Vol. 35, No. 2 | 25 July 2006AbstractPDF (848 KB) On The Complexity of Computing Mixed VolumesMartin Dyer, Peter Gritzmann, and Alexander HufnagelSIAM Journal on Computing, Vol. 27, No. 2 | 28 July 2006AbstractPDF (966 KB) Universal Approximation Using Feedforward Neural Networks: A Survey of Some Existing Methods, and Some New ResultsNeural Networks, Vol. 11, No. 1 | 1 Jan 1998 Cross Ref A unified approach to evaluation algorithms for multivariate polynomialsMathematics of Computation, Vol. 66, No. 220 | 1 January 1997 Cross Ref The Work of G. G. Lorentz on Birkhoff InterpolationMathematics from Leningrad to Austin | 1 Jan 1997 Cross Ref Multivariate InterpolationMathematics from Leningrad to Austin | 1 Jan 1997 Cross Ref Solvability problems of bivariate interpolation IMathematics from Leningrad to Austin | 1 Jan 1997 Cross Ref Solvability of Bivariate Interpolation II, ApplicationsMathematics from Leningrad to Austin | 1 Jan 1997 Cross Ref The Work of G. G. Lorentz on Birkhoff InterpolationMathematics from Leningrad to Austin | 1 Jan 1997 Cross Ref Multivariate InterpolationMathematics from Leningrad to Austin | 1 Jan 1997 Cross Ref Solvability problems of bivariate interpolation IMathematics from Leningrad to Austin | 1 Jan 1997 Cross Ref Solvability of Bivariate Interpolation II: ApplicationsMathematics from Leningrad to Austin | 1 Jan 1997 Cross Ref Design of an Essentially Nonoscillatory Reconstruction Procedure on Finite-Element-Type MeshesUpwind and High-Resolution Schemes | 1 Jan 1997 Cross Ref Network SplinesResults in Mathematics, Vol. 30, No. 3-4 | 17 April 2013 Cross Ref The optimal symmetrical points for polynomial interpolation of real functions in the tetrahedronComputer Methods in Applied Mechanics and Engineering, Vol. 137, No. 1 | 1 Oct 1996 Cross Ref A recursive algorithm for Hermite interpolation over a triangular gridJournal of Computational and Applied Mathematics, Vol. 73, No. 1-2 | 1 Oct 1996 Cross Ref Regular points for Lagrange interpolation on the unit diskNumerical Algorithms, Vol. 12, No. 2 | 1 Sep 1996 Cross Ref On multi-level bases for elliptic boundary value problemsJournal of Computational and Applied Mathematics, Vol. 71, No. 1 | 1 Jul 1996 Cross Ref Approximate optimal points for polynomial interpolation of real functions in an interval and in a triangleComputer Methods in Applied Mechanics and Engineering, Vol. 128, No. 3-4 | 1 Dec 1995 Cross Ref Interpolation on the Triangle and SimplexApproximation Theory, Wavelets and Applications | 1 Jan 1995 Cross Ref Polynomial Interpolation in Several VariablesStudies in Computer Science | 1 Jan 1994 Cross Ref Admissible Location of Sample Points of Interpolation by Bivariate C 1 Quadratic SplinesApproximation, Probability, and Related Fields | 1 Jan 1994 Cross Ref On the Complexity of Some Basic Problems in Computational ConvexityPolytopes: Abstract, Convex and Computational | 1 Jan 1994 Cross Ref Historical perspective on interpolation, approximation and quadratureHandbook of Numerical Analysis Volume 3 | 1 Jan 1994 Cross Ref Approximation and interpolation theoryHandbook of Numerical Analysis Volume 3 | 1 Jan 1994 Cross Ref Multivariate polynomial interpolation under projectivities II: Neville-Aitken formulasNumerical Algorithms, Vol. 2, No. 3 | 27 December 2013 Cross Ref Some Aspects of Radial Basis Function ApproximationApproximation Theory, Spline Functions and Applications | 1 Jan 1992 Cross Ref Construction of lattices for lagrange interpolation in projective spaceConstructive Approximation, Vol. 7, No. 1 | 1 Dec 1991 Cross Ref On bivariate osculatory interpolationJournal of Computational and Applied Mathematics, Vol. 38, No. 1-3 | 1 Dec 1991 Cross Ref Design of 2-D FIR filters by nonuniform frequency samplingIEEE Transactions on Signal Processing, Vol. 39, No. 11 | 1 Nov 1991 Cross Ref Multivariate polynomial interpolation under projectivities part I: lagrange and newton interpolation formulasNumerical Algorithms, Vol. 1, No. 3 | 1 Oct 1991 Cross Ref On certain configurations of points in Rn which are unisolvent for polynomial interpolationJournal of Approximation Theory, Vol. 64, No. 3 | 1 Mar 1991 Cross Ref A characterization of multivariate quasi-interpolation formulas and its applicationsNumerische Mathematik, Vol. 57, No. 1 | 1 Dec 1990 Cross Ref On multivariate polynomial interpolationConstructive Approximation, Vol. 6, No. 3 | 1 Sep 1990 Cross Ref On multivariate polynomial interpolationAlgorithms for Approximation II | 1 Jan 1990 Cross Ref A catalogue of algorithms for approximationAlgorithms for Approximation II | 1 Jan 1990 Cross Ref The use of Homogeneous Coordinates in Spline Functions and Polynomial InterpolationMultivariate Approximation and Interpolation | 1 Jan 1990 Cross Ref Multivariate Polynomial InterpolationComputation of Curves and Surfaces | 1 Jan 1990 Cross Ref A Finite Element Approach to Surface ReconstructionComputation of Curves and Surfaces | 1 Jan 1990 Cross Ref Local approximation by certain spaces of exponential polynomials, approximation order of exponential box splines, and related interpolation problemsTransactions of the American Mathematical Society, Vol. 319, No. 1 | 1 January 1990 Cross Ref Reconstruction of two-dimensional signals from level crossingsProceedings of the IEEE, Vol. 78, No. 1 | 1 Jan 1990 Cross Ref Two-dimensional nonuniform sampling expansions an iterative approach. ii. reconstruction formulae and applicationsApplicable Analysis, Vol. 32, No. 1 | 1 Jan 1989 Cross Ref Interpolation on the Simplex by Homogeneous PolynomialsNumerical Mathematics Singapore 1988 | 1 Jan 1988 Cross Ref UNISOLVENT INTERPOLATION IN IRn AND THE SIMPLICIAL POLYNOMIAL FINITE ELEMENT METHODTopics in Multivariate Approximation | 1 Jan 1987 Cross Ref A BIBLIOGRAPHY OF MULTIVARIATE APPROXIMATIONTopics in Multivariate Approximation | 1 Jan 1987 Cross Ref On Aitken-Neville Formulae for Multivariate InterpolationNumerical Approximation of Partial Differential Equations, Selection of Papers Presented at the International Symposium on NumericalAnalysis held at the Polytechnic University of Madrid | 1 Jan 1987 Cross Ref Solvability problems of bivariate interpolation IConstructive Approximation, Vol. 2, No. 1 | 1 Dec 1986 Cross Ref Osculatory Interpolation in Rⁿ J. R. BuschSIAM Journal on Numerical Analysis, Vol. 22, No. 1 | 14 July 2006AbstractPDF (665 KB) On Bivariate Vertex SplinesMultivariate Approximation Theory III | 1 Jan 1985 Cross Ref Multivariate interpolationRational Approximation and Interpolation | 9 September 2006 Cross Ref A Note on Recurrence Interpolation Formulae for Certain Sets of Points in RkNumerical Methods of Approximation Theory, Vol. 7 / Numerische Methoden der Approximationstheorie, Band 7 | 1 Jan 1983 Cross Ref On the linear independence of multivariate 𝐵-splines. II. Complete configurationsMathematics of Computation, Vol. 41, No. 163 | 1 January 1983 Cross Ref On Lagrange and Hermite interpolation in R kNumerische Mathematik, Vol. 39, No. 1 | 1 Feb 1982 Cross Ref Topics in multivariate approximation theoryTopics in Numerical Analysis | 25 August 2006 Cross Ref On the complexity of quantum ACCProceedings 15th Annual IEEE Conference on Computational Complexity Cross Ref Volume 14, Issue 4| 1977SIAM Journal on Numerical Analysis575-778 History Submitted: 20 February 1973Published online: 14 July 2006 InformationCopyright © 1977 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI: 10. 1137/0714050Article page range: pp. 735-743ISSN (print): 0036-1429ISSN (online): 1095-7170Publisher: Society for Industrial and Applied Mathematics