Abstract
We construct local L-splines that have an arbitrary arrangement of knots and preserve the kernel of a linear differential operator L of order r with constant coefficients and real pairwise distinct roots of the characteristic polynomial.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Yu. S. Zav’yalov, B. I. Kvasov, and V. L. Miroshnichenko, Methods of Spline Functions (Nauka, Moscow, 1980).
T. Lyche and L. L. Schumaker, “Local spline approximation methods,” J. Appr. Theory 15(4), 294–325 (1975).
E. V. Shevaldina, “Approximation by local L-splines of even order preserving the kernel of a differential operator,” Izv. Tul’sk. Gos. Univ. 2, 62–73 (2009).
E. V. Shevaldina, “Local L-splines preserving the kernel of a differential operator,” Sib. Zh. Vychisl. Mat. 13(1), 111–121 (2010).
E. V. Strelkova and V. T. Shevaldin, “Approximation by local L-splines that are exact on subspaces of the kernel of a differential operator,” Proc. Steklov Inst. Math. 273(Suppl. 1), S133–S141 (2011).
E. V. Strelkova and V. T. Shevaldin, “Form preservation under approximation by local exponential splines of an arbitrary order,” Proc. Steklov Inst. Math. 277(Suppl. 1), S171–S180 (2012).
Yu. S. Volkov, E. G. Pytkeev, and V. T. Shevaldin, “Orders of approximation by local exponential splines,” Proc. Steklov Inst. Math. 284(Suppl. 1), S175–S184 (2014).
V. T. Shevaldin, “Approximation by local parabolic splines with an arbitrary arrangement of knots,” Sib. Zh. Vychisl. Mat. 8(1), 77–88 (2005).
Yu. N. Subbotin, “Approximations by polynomial and trigonometric splines of third order preserving some properties of approximated functions,” Proc. Steklov Inst. Math., Suppl. 2, S231–S242 (2007).
Yu. S. Volkov, E. V. Strelkova, and V. T. Shevaldin, “Local approximation by splines with displacement of nodes,” Siberian Adv. Math. 23(1), 69–75 (2011).
A. Sharma and I. Cimbalario, “Certain linear differential operators and generalized differences,” Math. Notes 21(2), 91–97 (1977).
T. Popoviciu, “Sur le reste dans certains formules lineares d’approximation de l’analyse,” Mathematica (Cluj) 1, 95–142 (1959).
Z. Wronicz, Chebyshevian Splines (Inst. Mat. Polska Akad. Nauk, Warsaw, 1990), Ser. Dissertationes Math., Vol. 305.
G. Muhlbach, “A recurrence formula for generalized divided differences and some applications,” J. Approx. Theory 9(2), 165–172 (1973).
G. Walz, “Generalized divided differences, with applications to generalized B-splines,” Calcolo 29(1-2), 111–123 (1992).
G. Pólya and G. Szegö,, Problems and Theorems in Analysis (Springer-Verlag, Berlin, 1972; Nauka, Moscow, 1978), Vol. 2.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © E.V. Strelkova, V.T. Shevaldin, 2014, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Vol. 20, No. 1
Rights and permissions
About this article
Cite this article
Strelkova, E.V., Shevaldin, V.T. Local exponential splines with arbitrary knots. Proc. Steklov Inst. Math. 288 (Suppl 1), 189–194 (2015). https://doi.org/10.1134/S0081543815020194
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0081543815020194