J. H. Ahlberg, E. N. Nilson, J. L. Walsh,
... of investigation, [1]-[26], into the properties of spline functions. These functions, which in their simplest form ... 25], and completeness [25] of certain bases of splines, are at first rather surprising. A few (cf. [ ... 241]) are still quite puzzling. The application of spline theory to the approximation of a function analytic ... an earlier paper, [24], by the authors. There splines were treated which are piecewise polynomial in the ... curve. The present development is concerned with cubic splines in the complex variable z and provides some ...
Tópico(s): Iterative Methods for Nonlinear Equations
1967 - American Mathematical Society | Transactions of the American Mathematical Society
... and , J. L. Walsh, Fundamental properties of generalized splines, Proc. Nat. Acad. Sci. U.S.A., 52 ( ... and , J. L. Walsh, Convergence properties of generalized splines, Proc. Nat. Acad. Sci. U.S.A., 54 ( ... Previous article Next article FiguresRelatedReferencesCited byDetails Complex Cubic Splines Cross Ref On Hermite-Birkhoff Interpolation Cross Ref ... 13, No. 1 Cross Ref Lacunary interpolation by splines (0; 0, 2, 3) and (0; 0, 2, ... 4 Cross Ref On best cubature formulas and spline interpolationNumerische Mathematik, Vol. 32, No. 3 Cross Ref ...
Tópico(s): Heat Transfer and Numerical Methods
1966 - Society for Industrial and Applied Mathematics | SIAM Journal on Numerical Analysis
... Nilson and , J. L. Walsh, The theory of splines and their applications, Academic Press, New York, 1967xi+ ... 0158.15901 Google Scholar[2] Garrett Birkhoff, Local spline approximation by moments, J. Math. Mech., 16 (1967), ... 3] Carl de Boor, On uniform approximation by splines, J. Approximation Theory, 1 (1968), 219–235 10. ... de Boor, On the convergence of odd-degree spline interpolation, J. Approximation Theory, 1 (1968), 452–463 ... 11001 CrossrefGoogle Scholar[8] J. Nitsche, Umkehrsätze für Spline-Approximationen, Compositio Math., 21 (1969), 400–416 MR0259436 ...
Tópico(s): Advanced Numerical Analysis Techniques
1970 - Society for Industrial and Applied Mathematics | SIAM Journal on Numerical Analysis
Joseph W. Jerome, Larry L. Schumaker,
... article Next article A Note on Obtaining Natural Spline Functions by the Abstract Approach of Atteia and ... Etude de certains noyaux et théorie des fonctions "spline" en analyse numerique, Doctoral thesis, University of Grenoble, ... Schoenberg, On Pólya frequency functions. IV. The fundamental spline functions and their limits, J. Analyse Math., 17 ( ... 3] Carl de Boor, Best approximation properties of spline functions of odd degree, J. Math. Mech., 12 ( ... N. E. Greville, Numerical procedures for interpolation by spline functions, J. Soc. Indust. Appl. Math. Ser. B ...
Tópico(s): Advanced Numerical Methods in Computational Mathematics
1968 - Society for Industrial and Applied Mathematics | SIAM Journal on Numerical Analysis
Next article Uniform Approximation by Chebyshev Spline Functions. II: Free KnotsLarry SchumakerLarry Schumakerhttps://doi.org/10.1137/0705051PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Carl H. Fitzgerald and , ... Scholar[5] Samuel Karlin and , Zvi Ziegler, Chebyshevian spline functions, SIAM J. Numer. Anal., 3 (1966), 514– ... On some approximation problems involving Tchebycheff systems and spline functions, Doctoral thesis, Stanford University, Stanford, California, 1966 ...
Tópico(s): Iterative Methods for Nonlinear Equations
1968 - Society for Industrial and Applied Mathematics | SIAM Journal on Numerical Analysis
Springer Link
... On the Order of Convergence of Natural Cubic Spline InterpolationKendall E. AtkinsonKendall E. Atkinsonhttps://doi.org/10. ... and , E. N. Nilson, Convergence properties of the spline fit, J. Soc. Indust. Appl. Math., 11 (1963), ... Birkhoff and , Carl de Boor, Error bounds for spline interpolation, J. Math. Mech., 13 (1964), 827–835 ... 3] Carl de Boor, Best approximation properties of spline functions of odd degree, J. Math. Mech., 12 ( ... 0111.06003 Google Scholar[5] I. J. Schoenberg, Spline interpolation and best quadrature formulae, Bull. Amer. Math. ...
Tópico(s): Numerical Methods and Algorithms
1968 - Society for Industrial and Applied Mathematics | SIAM Journal on Numerical Analysis
... New Methods and Results Cross Ref Zeros of Splines and Birkhoff’s Kernel Cross Ref Birkhoff Quadrature ... Ref References Cross Ref Total Positivity of the Spline Kernel and its Applications Cross Ref Approximation and ... formulasCalcolo, Vol. 26, No. 1 Cross Ref B-splines with Birkhoff knotsConstructive Approximation, Vol. 4, No. 1 Cross Ref σ-Perfect splines and their application to optimal recovery problemsJournal of ... KB)The Budan-Fourier theorem and Hermite-Birkhoff spline interpolation1 January 1982 | Transactions of the American Mathematical ...
Tópico(s): Coding theory and cryptography
1969 - Society for Industrial and Applied Mathematics | SIAM Journal on Numerical Analysis
... Walsh, Extremal, orthogonality, and convergence properties of multidimensional splines, J. Math. Anal. Appl., 12 (1965), 27–48 ... Nilson and , J. L. Walsh, The theory of splines and their applications, Academic Press, New York, 1967xi+ ... Carl de Boor and , Robert E. Lynch, On splines and their minimum properties, J. Math. Mech., 15 ( ... algorithms for the computation of interpolating and approximating spline functions, Theory and Applications of Spline Functions (Proceedings of Seminar, Math, Research Center, Univ. ...
Tópico(s): Advanced Numerical Analysis Techniques
1971 - Society for Industrial and Applied Mathematics | SIAM Journal on Numerical Analysis
... Nilson and , J. L. Walsh, The theory of splines and their applications, Academic Press, New York, 1967xi+ ... 06003 Google Scholar[11] Carl de Boor, Bicubic spline interpolation, J. Math. and Phys., 41 (1962), 212– ... Carl de Boor and , Robert E. Lynch, On splines and their minimum properties, J. Math. Mech., 15 ( ... to appear Google Scholar[16] William J. Gordon, Spline-blended surface interpolation through curve networks, J. Math. ... approximation of multivariate functionsApproximations with Special Emphasis on Spline Functions (Proc. Sympos. Univ. of Wisconsin, Madison, Wis., ...
Tópico(s): Heat Transfer and Numerical Methods
1971 - Society for Industrial and Applied Mathematics | SIAM Journal on Numerical Analysis
Blair Swartz, Richard S. Varga,
... here is to obtain improved error bounds for spline and L-spline interpolation at knots, and to obtain certain stability ( ... defined on [a, b] by a smooth cubic spline s over a uniform partition A, of [a, ... E Cl[u, b], then its unique cubic spline interpolant s is defined by
Tópico(s): Advanced Numerical Analysis Techniques
1972 - Elsevier BV | Journal of Approximation Theory
Daniel B. Suits, Andrew Mason, Louis K.C. Chan,
... the adopting discipline. A recent example is the spline function. Briefly put, spline functions are a device for approximating the shape ... over from engineering and the mathematics of interpolation, spline functions have appeared in several places in economic ... 1973, 1976). Buse and Lim (1977) have shown spline functions to be a special case of restricted ... even in some of the work where the spline function has been employed, it has not always ... might improve their analysis to employ a multivariate spline function, were constrained by the fact that the ...
Tópico(s): Monetary Policy and Economic Impact
1978 - The MIT Press | The Review of Economics and Statistics
The cubic X-spline is a generalization of the conventional cubic spline in which the second derivative is allowed to possess discontinuities at ... to illustrate the usefulness of the cubic X-spline it is applied to the classical interpolation problem and compared with the conventional cubic spline. It is shown that the free parameters may ...
Tópico(s): Tribology and Lubrication Engineering
1978 - Oxford University Press | IMA Journal of Applied Mathematics
... No. 1 | 26 April 2016 Cross Ref Quartic splines on Powell–Sabin triangulationsComputer Aided Geometric Design, Vol. ... Vol. 310 | 1 Apr 2016 Cross Ref Trivariate spline quasi-interpolants based on simplex splines and polar formsMathematics and Computers in Simulation, Vol. ... Cross Ref Superconvergent $$C^1$$ C 1 cubic spline quasi-interpolants on Powell-Sabin partitionsBIT Numerical Mathematics, ... 26 July 2014 Cross Ref Superconvergent trivariate quadratic spline quasi-interpolants on Worsey–Piper splitJournal of Computational ...
Tópico(s): Composite Structure Analysis and Optimization
1977 - Society for Industrial and Applied Mathematics | SIAM Journal on Numerical Analysis
... extension of the notion of an L-g spline, three mathematical structures called LM-g splines of types I, II, and III are introduced. ... 0, T]. Each of the above types of splines is the solution of an optimization problem more ... used in the definition of the L-g spline and hence it is recognized as an entity ... and more general mathematically than the L-g spline. The LM-g splines introduced here reduce to an L-g spline in the special case in which m = 0 ... characterization, and best approximation properties for the proposed splines are obtained in an appropriate reproducing kernel Hilbert ...
Tópico(s): Composite Structure Analysis and Optimization
1977 - Elsevier BV | Journal of Approximation Theory
... paper presents an algorithm for fitting a smoothing spline function to a set of experimental or tabulated data. The obtained spline approximation can be used for differentiation and integration ... the good conditioning properties we use normalised B-splines to represent the smoothing spline. A Fortran implementation ...
Tópico(s): Iterative Methods for Nonlinear Equations
1975 - Elsevier BV | Journal of Computational and Applied Mathematics