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spline functions


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1: 24.17 Mathematical Applications
§24.17(ii) Spline Functions
The members of 𝒮 n are called cardinal spline functions. The functions
24.17.3 S n ( x ) = E ~ n ( x + 1 2 n + 1 2 ) E ~ n ( 1 2 n + 1 2 ) , n = 0 , 1 , ,
Bernoulli Monosplines
2: 3.11 Approximation Techniques
The set of all the polynomials defines a function, the spline, on [ a , b ] . … For many applications a spline function is a more adaptable approximating tool than the Lagrange interpolation polynomial involving a comparable number of parameters; see §3.3(i), where a single polynomial is used for interpolating f ( x ) on the complete interval [ a , b ] . Multivariate functions can also be approximated in terms of multivariate polynomial splines. …
3: Bibliography S
  • L. L. Schumaker (1981) Spline Functions: Basic Theory. John Wiley & Sons Inc., New York.
  • 4: 3.3 Interpolation
    §3.3(vi) Other Interpolation Methods
    For Hermite interpolation, trigonometric interpolation, spline interpolation, rational interpolation (by using continued fractions), interpolation based on Chebyshev points, and bivariate interpolation, see Bulirsch and Rutishauser (1968), Davis (1975, pp. 27–31), and Mason and Handscomb (2003, Chapter 6). … For interpolation of a bounded function f on the cardinal function of f is defined by …is called the Sinc function. …
    5: Publications
  • B. V. Saunders and Q. Wang (2006) From B-Spline Mesh Generation to Effective Visualizations for the NIST Digital Library of Mathematical Functions, in Curve and Surface Design, Proceedings of the Sixth International Conference on Curves and Surfaces, Avignon, France June 29–July 5, 2006, pp. 235–243. PDF
  • B. Saunders and Q. Wang (2010) Tensor Product B-Spline Mesh Generation for Accurate Surface Visualizations in the NIST Digital Library of Mathematical Functions, in Mathematical Methods for Curves and Surfaces, Proceedings of the 2008 International Conference on Mathematical Methods for Curves and Surfaces (MMCS 2008), Lecture Notes in Computer Science, Vol. 5862, (M. Dæhlen, M. Floater., T. Lyche, J. L. Merrien, K. Mørken, L. L. Schumaker, eds), Springer, Berlin, Heidelberg (2010) pp. 385–393. PDF
  • 6: Bibliography M
  • I. G. Macdonald (1990) Hypergeometric Functions.
  • B. Markman (1965) Contribution no. 14. The Riemann zeta function. BIT 5, pp. 138–141.
  • F. Matta and A. Reichel (1971) Uniform computation of the error function and other related functions. Math. Comp. 25 (114), pp. 339–344.
  • D. S. Meek and D. J. Walton (1992) Clothoid spline transition spirals. Math. Comp. 59 (199), pp. 117–133.
  • S. C. Milne (2002) Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions. Ramanujan J. 6 (1), pp. 7–149.
  • 7: Bibliography C
  • B. C. Carlson (1985) The hypergeometric function and the R -function near their branch points. Rend. Sem. Mat. Univ. Politec. Torino (Special Issue), pp. 63–89.
  • B. C. Carlson (2006b) Table of integrals of squared Jacobian elliptic functions and reductions of related hypergeometric R -functions. Math. Comp. 75 (255), pp. 1309–1318.
  • C. K. Chui (1988) Multivariate Splines. CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 54, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
  • R. Cicchetti and A. Faraone (2004) Incomplete Hankel and modified Bessel functions: A class of special functions for electromagnetics. IEEE Trans. Antennas and Propagation 52 (12), pp. 3373–3389.
  • A. P. Clarke and W. Marwood (1984) A compact mathematical function package. Australian Computer Journal 16 (3), pp. 107–114.
  • 8: Bibliography D
  • H. T. Davis (1933) Tables of Higher Mathematical Functions I. Principia Press, Bloomington, Indiana.
  • C. de Boor (2001) A Practical Guide to Splines. Revised edition, Applied Mathematical Sciences, Vol. 27, Springer-Verlag, New York.
  • A. Dienstfrey and J. Huang (2006) Integral representations for elliptic functions. J. Math. Anal. Appl. 316 (1), pp. 142–160.
  • K. Dilcher (2002) Bernoulli Numbers and Confluent Hypergeometric Functions. In Number Theory for the Millennium, I (Urbana, IL, 2000), pp. 343–363.
  • A. J. Durán (1993) Functions with given moments and weight functions for orthogonal polynomials. Rocky Mountain J. Math. 23, pp. 87–104.