APPROXIMATION AND SMOOTHING OF A FUNCTION BASED ON GODUNOV REGULARIZATION

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Abstract

A new approach to function approximation is presented, based on S.K. Godunov’s ideas on the regularization of ill-conditioned systems. The proposed method allows for determining function values at nodes of a finer grid from data on a coarser grid while ensuring control over the smoothness of the resulting function. Convergence and smoothness estimates are substantiated, and results from computational experiments illustrate the effectiveness of the proposed method.

About the authors

E. A Biberdorf

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Email: math@biberdorf.ru
Novosibirsk, Russia

K. K Abdisheripov

Novosibirsk State University

Novosibirsk, Russia

References

  1. Годунов С.К., Антонов А.Г., Кирилюк О.П., Костин В.И. Гарантированная точность решения систем линейных уравнений в евклидовых пространствах. Новосибирск: Наука, 1988. С. 456.
  2. Бибердорф Э.А., Попова Н.И. Гарантированная точность современных алгоритмов линейной алгебры. Новосибирск: Изд-во СО РАН, 2006. С. 319.
  3. Кабанихин С.И. Обратные и некорректные задачи. Новосибирск: Сиб. науч. изд-во, 2009. C. 458.
  4. Годунов С.К. Современные аспекты линейной алгебры. Новосибирск: Науч. книга, 1997. C. 388.

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