On Best Error Bounds for Approximations by Algebraic Polynomials and Splines in the Spaces and
An analog of the well-known Jackson–Bernstein theory on best approximation by trigonometric polynomials is developed for approximation methods which use algebraic polynomials and piecewise polynomial functions on a finite interval. Approximation errors are measured in the norms of the Sobolev space...
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| Veröffentlicht in: | Lobachevskii journal of mathematics 2022, Vol.43 (11), p.3091-3103 |
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| container_issue | 11 |
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| container_title | Lobachevskii journal of mathematics |
| container_volume | 43 |
| creator | Dautov, R. Z. |
| description | An analog of the well-known Jackson–Bernstein theory on best approximation by trigonometric polynomials is developed for approximation methods which use algebraic polynomials and piecewise polynomial functions on a finite interval. Approximation errors are measured in the norms of the Sobolev space
and Besov space
. These results can be useful in error analysis of the spectral,
-, and
- finite element methods for solving differential equations. |
| doi_str_mv | 10.1134/S1995080222140086 |
| format | Article |
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| fulltext | fulltext |
| identifier | ISSN: 1995-0802 |
| ispartof | Lobachevskii journal of mathematics, 2022, Vol.43 (11), p.3091-3103 |
| issn | 1995-0802 1818-9962 |
| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Algebra Analysis Approximation Differential equations Error analysis Finite element method Function space Geometry Mathematical analysis Mathematical Logic and Foundations Mathematics Mathematics and Statistics Norms Polynomials Probability Theory and Stochastic Processes Sobolev space Spline functions |
| title | On Best Error Bounds for Approximations by Algebraic Polynomials and Splines in the Spaces and |
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