Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Khromova G. V. Discontinuous Steklov operator and approximate polynomial splines. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2025, vol. 25, iss. 2, pp. 184-188. DOI: 10.18500/1816-9791-2025-25-2-184-188, EDN: ETQAWZ

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
30.05.2025
Full text:
download
(downloads: 443)
Language: 
Russian
Heading: 
Mathematics
Article type: 
Article
UDC: 
517.51
DOI: 
10.18500/1816-9791-2025-25-2-184-188
EDN: 
ETQAWZ

Discontinuous Steklov operator and approximate polynomial splines

Autors: 
Khromova Galina Vladimirovna, Saratov State University
Abstract: 

For a continuous function specified on a uniform grid of the segment [0,1], a method for constructing approximation polynomial splines is presented. This method does not require any additional information about the function and ensures uniform convergence. This convergence also occurs for an approximately given grid function. In the case of a parabolic spline, the article provides formulas ready for direct use.

Key words: 
Steklov operator
broken line
continuous function
uniform mesh
uniform approximations
spline
References: 
  1. Stechkin S. B., Subbotin Yu. N. Splayny v vychislitel’noy matematike [Splines in computational mathematics]. Moscow, Nauka, 1976. 248 p. (in Russian).
  2. Starkov V. N. Konstruktivnye metody vychislitel’noy fiziki v zadachakh interpretatsii [Constructive methods of computational physics in interpretation problems]. Kiev, Naukova Dumka, 2002. 262 p. (in Russian).
  3. Khromova G. V. Operators with discontinuous range and their applications. Progress in Science and Technology. Contemporary Mathematics and its Applications. Thematic Surveys, 2021, vol. 200, pp. 58–64 (in Russian). https://doi.org/10.36535/0233-6723-2021-200-58-64, EDN: MJEHGK
  4. Khromova G. V. Discontinuous Steklov operator and polynomial splines. Contemporary Problems of Function Theory and Their Applications, 2024, iss. 22, pp. 296–299 (in Russian). EDN: XXTNRH
  5. Khromova G. V. An analogue of interpolation parabolic splines. Trudy Matematicheskogo tsentra im. N. I. Lobachevskogo [Proceedings of the N. I. Lobachevsky Mathematical Center], 2023, vol. 66, pp. 279–281 (in Russian).
  6. Sovetnikova S. Yu. On restoring functions defined on a grid. Contemporary Problems of Function Theory and Their Applications, 2024, iss. 22, pp. 252–255 (in Russian). EDN: DHPJAU
Received: 
06.05.2024
Accepted: 
11.12.2024
Published: 
30.05.2025
  • 769 reads