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A sharp error estimate of the best approximation by algebraic polynomials in the weighted space L 2(−1, 1)

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Abstract

We obtain an exact error estimate of the best approximation by algebraic polynomials in the Lebesgue space L 2(−1, 1) with the weight 1 − x 2 of degree λ > −1.

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References

  1. C. Schwab, p- and hp-Finite Element Methods: Theory and Applications to Solid and Fluid Mechanics (Oxford University Press, Oxford, 1999).

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Authors and Affiliations

  1. Kazan (Volga Region) Federal University, ul. Kremlyovskaya 18, Kazan, 420008, Russia

    R. Z. Dautov

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  1. R. Z. Dautov
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Correspondence to R. Z. Dautov.

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Original Russian Text © R.Z. Dautov, 2013, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, No. 5, pp. 61–63.

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Dautov, R.Z. A sharp error estimate of the best approximation by algebraic polynomials in the weighted space L 2(−1, 1). Russ Math. 57, 51–53 (2013). https://doi.org/10.3103/S1066369X1305006X

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  • DOI: https://doi.org/10.3103/S1066369X1305006X

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