Numerical evaluation of Cauchy principal value integrals by means of nodal spline approximation

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  • Caterina Dagnino Universita di Torino, Italy
  • Elisabetta Santi Universita di Decce, Italy
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References

C.Dagnino, V.Demichelis and E.Santi, Numerical integration based on quasi-interpolating splines, Computing 50 (1993), 146-163, https://doi.org/10.1007/bf02238611

C. Dagnino, V. Demichelis and E. Santi, Local spline approximation methods for singular product integration, J. Appr.Theory and its Appl. 12 (1996), 37-51.

W. Dahmen, T.N.T. Goodman and C.A. Micchelli, Compactly supported fundamental functions for spline interpolation, Numer. Math. 52 (1988), 641-644.

P.J. Davis and P. Rabinowitz, Methods of Numerical Integration, Academic Press, New York, 1984.

J.M. De Villiers and C.H. Rohwer, Optimal local spline interpolants, J. Comp. Appl. Math. 18 (1987), 107-119, https://doi.org/10.1016/0377-0427(87)90059-8

J.M. De Villiers and C.H. Rohwer, A nodal spline generalization of the Lagrange interpolant, Progress in Appr. Theory (P.Nevai and A.Pinkus, Eds.), Academic Press, San Diego (1991), 201-211.

J.M. De Villiers, A convergence result in nodal spline interpolation, J.Approx. Theory 74 (1993), 266-279, https://doi.org/10.1006/jath.1993.1066

J.M. De Villiers and C.H. Rohwer, Sharp bounds for the Lebesgue constant in quadratic nodal spline interpolation, Intern. Series of Num. Math. 115 (1994), 1-13.

A. Erdelèyi, W.Magnus, F.Oberhettinger and F.G.Tricomi, Tables of integral transforms, Vol. II Mc Graw Hill, New York, 1954.

T. Lyche and L.L. Schumaker, Local spline approximation methods, J. Appr. Theory 15 (1975), 294-325, https://doi.org/10.1016/0021-9045(75)90091-x

P. Rabinowitz and I.H.Sloan, Product integration in the presence of a singularity, SIAM J. Numer. Anal. 21 (1984), 144-166, https://doi.org/10.1137/0721010

P. Rabinowitz, On the convergence of closed interpolatory integration rule based on zeros of Gegenbauer polynomials, J. Comp. Appl. Math. 17 (1987), 43-46, https://doi.org/10.1016/0377-0427(87)90037-9

P. Rabinowitz, Numerical integration based on approximating spline, J. Comp. Appl. Math. 33 (1990), 73-83, https://doi.org/10.1016/0377-0427(90)90257-z

P. Rabinowitz, Product integration of singular integrands using optimal nodal spline, Rend. Sem. Mat. Univ. Pol. Torino 51 (1993), 1-9.

E. Santi, On the evaluation of Cauchy principal value integrals by rules based on quasi-interpolating splines, J. Comp. Appl. Math. 71 (1996), 1-14, https://doi.org/10.1016/0377-0427(95)00213-8

L.L.Schumaker, Spline Functions, John Wiley & Sons 1981.

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Published

1998-02-01

How to Cite

Dagnino, C., & Santi, E. (1998). Numerical evaluation of Cauchy principal value integrals by means of nodal spline approximation. Rev. Anal. Numér. Théor. Approx., 27(1), 59–69. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/1998-vol27-no1-art7

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Vol. 27 No. 1 (1998)

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