Numerical evaluation of Cauchy principal value integrals based on local spline approximation operators

Journal of Computational and Applied Mathematics

Volumn 76, Issue 1-2, 1996, Pages 231-238

  Dagnino, C ^a   Lamberti, P ^a  

^a UNIVERSITY OF TURIN   (Italy)

Author keywords

Approximating splines; B splines; Cauchy singular integrals

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; FUNCTIONS; MATHEMATICAL OPERATORS;

B SPLINES; CAUCHY PRINCIPAL VALUE INTEGRALS; LOCAL SPLINE APPROXIMATION METHODS;

INTEGRAL EQUATIONS;

EID: 0030393875     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(96)00105-7     Document Type: Article

References (14)

1. C. Dagnino, V. Demichelis and E. Santi, Numerical integration based on quasi-interpolating splines, Computing 50 (1993) 149-163.
2. C. Dagnino, V. Demichelis and E. Santi, An algorithm for numerical integration based on quasi-interpolating splines, Numer. Algorithms 5 (1993) 443-452.
3. C. Dagnino and P. Rabinowitz, Product integration of singular integrands based on quasi-interpolating splines, Comput. Math. to appear, special issue dedicated to 100 birthday of Cornelius Lanczos.
4. C. Dagnino, V. Demichelis and E. Santi, Local spline approximation methods for singular product integration, Approx. Theory Appl. 12 (1996) 1-14.
5. C. de Boor, A Practical Guide to Splines, Applied Mathematical Sciences, Vol. 27 (Springer, Berlin, 1978).
6. V. Demichelis, The use of modified quasi-interpolating splines for the solution of Prandtl equation, J. Comput. Appl. Math. 59 (1996) 329-338.
7. V. Demichelis, Quasi-interpolatory splines based on Schoenberg points, Math. Comput. 65 n.215 (1996) 1235-1247.
8. T. Lyche and L.L. Schumaker, Local spline approximation methods, J. Approx. Theory 15 (1975) 294-325.
9. P. Rabinowitz, Numerical integration based on approximating splines, J. Comput. Appl. Math. 33 (1990) 73-83.
10. P. Rabinowitz, Application of approximating splines for the solution of Cauchy singular integral equations, Appl. Numer. Math. 15 (1994) 285-297.
11. P. Rabinowitz and E. Santi, On the uniform convergence of Cauchy principal value of quasi-interpolating splines, Bit 35 (1995) 277-290.
12. P. Rabinowitz, Numerical evaluation of Cauchy principal value integrals with singular integrands, Math. Comput. 55 (1990) 265-276.
13. L.L. Schumaker, Spline Functions (Wiley, New York, 1981).
14. G. Szegö, Orthogonal Polynomials, AMS Colloq. Publications, Vol. XXIII, 1939.