On some application of biorthogonal spline systems to integral equations

• Autorzy: Wronicz Z.
• Języki publikacji: EN

Abstrakty

EN

We consider an operator PN : LP(I) -> Sn(deltaN), such that PN f = f for f mem Sn(deltaN), where Sn(deltaN) is the space of splines of degree n with repect to a given partition deltaN of the interval I. This operator is defined by means of a system of step functions biorthogonal to B-splines. Then we use this operator to approximation to the solution of the Fredholm integral equation of the second kind. Convergence rates for the aproximation of the solution of this equation are given.

Słowa kluczowe

EN

operator associated with step functions; B-splines; integral equation; approximation

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2005
• Tom: Vol. 25, no. 1
• Strony: 149--160
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Wronicz Z.

• AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Cracow, Poland,

Bibliografia

• [1] Atkinson K.: The numerical solution of integral equations of the second kind. Cambridge, Cambridge University Press 1997.
• [2] Atkinson K., Han W.: Theoretical numerical analysis. New York, Springer-Verlag 2001.
• [3] Berezin I.S., Zhidkov N.P.: Numerical methods, vol. II, Moskva 1962 (Russian).
• [4] de Boor C.: On local linear functionals which vanish at all B-splines but one. In: Theory of Approximation with Applications, Law A., Sahney A. (Eds), New York, Academic Press 1976, 120-145.
• [5] de Boor C.: Splines as linear combinations of B-splines. In: Approximation Theory II, Lorenz G. G., Chui C. K., Schumaker L. L. (Eds), New York, Academic Press 1976, 1-47.
• [6] Ciesielski Z.: Constructive function theory and spline systems. Studia Math. 53 (1975), 278-302.
• [7] Ciesielski Z.: Lectures on Spline Theory. Gdańsk University, 1979 (Polish).
• [8] Curry H. B., Schoenberg I.J.: IV: The fundamental spline functions and their limits. J. d'Analyse Math. 17 (1966), 71-107.
• [9] Krasnov M.L., Kiselev A. I., Makarenko G.I.: Problems in integral equations. Warszawa, PWN 1972 (Polish).
• [10] Michlin S.G., Smolicki C.L.: Methods of approximation of the solution of diffe­rential and integral equations. Warszawa 1972 (Polish).
• [11] Petrovskii I.G.: Lectures on the theory of integral equations. Moscow 1984 (Rus­sian).
• [12] Subbotin Yu.N., Stechkin S.B.: Splines in the Numerical Analysis. Moscow, Nauka 1976 (Russian).
• [13] Wronicz Z.: Approximation by complex splines. Zeszyty Nauk. Uniw. Jagielloń­skiego, Prace Mat. 20 (1979), 67-88.
• [14] Wronicz Z.: Systems conjugate to biorthogonal spline systems. Bull. Polish Acad. Sci. Math. 36 (1988), 273-278.
• [15] Wronicz Z.: On some complex spline operators. Opuscula Mathematica 23 (2003), 99-115.