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Original Articles

Computational Aspects Of Numerical Integration Based On Optimal Nodal Splines

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Pages 243-255 | Published online: 15 Sep 2010

  • Dagnino , C. and Demichelis , V . 2002 . Nodal splines integration rules for certain 2-D Cauchy principal value integrals . Intern. J. Computer Math. , 79 (2} ) : 233 – 246 .
  • Dagnino , C. , Demichelis , V. and Santi , E. 1993 . Numerical integration based on quasi-interpolating splines . Computing , 50 : 149 – 163 .
  • Dagnino , C. , Demichelis , V and Santi , E. 1996 . Local spline approximation methods for singular product integration . Approx. Theory and its Appl. , 12 : 37 – 51 .
  • De Boor , C. 1983 . A Practical Guide to Splines , Applied Mathematical Sciences 27 New York : Springer Verlag .
  • Demichelis , V . 1997 . Convergence of derivatives of optimal nodal splines . J. Approx. Theory , 88 : 370 – 383 .
  • De Villiers , J. M. 1993 . A convergence result in nodal spline interpolation . J. Approx. Theory , 74 : 266 – 279 .
  • De Villiers , J. M. and Rohwer , C. H. 1987 . Optimal local spline interpolants . J. Camp. Appl. Math. , 18 : 107 – 119 .
  • De Villiers , J. M. and Rohwer , C. H. 1991 . “ A nodal spline generalization of the Lagrange interpolant ” . In Progress in Approximation Theory , Edited by: Nevai , P. and Pinkus , A. 201 – 211 . Boston : Academic Press .
  • De Villiers , J. M. and Rohwer , C. H. 1994 . Sharp bounds for the Lebesgue constant in quadratic nodal spline interpolation . Intern. Series of Num. Math. , 115 : 1 – 13 .
  • Gerasoulis , A. 1986 . Piecewise-polynomial quadratures for Cauchy singular integrals . SlAM J. Numer. Anal. , 23 : 891 – 902 .
  • Gradshteiyn , I. S. and Ryxhik , I. M. 1965 . Tables of Integrals, Series and Products , New York : Academic Press .
  • Kutt , H. R. 1975 . The numerical evaluation of principal value integrals by finite-part integration . Numer. Math. , 24 : 205 – 210 .
  • Lyche , T. and Schumaker , L. L. 1975 . Local spline approximation methods . J. Approx. Theory , 15 : 294 – 325 .
  • Monegato , G. 1994 . The numerical evaluation of a 2-D Cauchy principal value integral arising in boundary integral equation methods . Math. Comp. , 62 : 775 – 777 .
  • Rabinowitz , P. 1990 . Numerical integration based on approximating splines . J. Comp. Appl. Math. , 33 : 73 – 83 .
  • Rabinowitz , P. 1993 . Product integration of singular integrals using optimal nodal splines . Rend. Sem. Mat. Univ. Pol. Torino , 51 (1} ) : 1 – 9 .
  • Rabinowitz , P. and Santi , E. 1995 . On the uniform convergence of Cauchy principal values of quasi-interpolating splines . BIT , 35 : 277 – 290 .

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