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Some Remarks on Product Approximations

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Multivariate Approximation Theory II

Abstract

Recently there has been considerable interest in various aspects, extensions, and variations of uniform product approximations (see [2,3,6,7] and the references of [3]), This paper concerns convergence and error bounds for polynomial product approximation and a variation similar to appolation considered in [6].

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References

  1. Cheney, E.W., “Introduction to Approximation Theory,” McGraw-Hill, New York, 1966.

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  2. Henry, M.S. and Schmidt, D., Continuity theorems for the product approximation operator, in “Theory of Approximation with Applications” (A.G. Law and B.N. Sahney, Eds.), pp.24–42, Academic Press, New York, 1976.

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  3. Henry, M.S. and Schmidt, D., Error bounds for polynomial product approximation, J. Approx. Theory 31(1981), pp. 6–21.

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  4. Larsen, R., “Functional Analysis,” Marcel Dekker, Inc., New York, 1973.

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  5. Rivlin, T.J., “An Introduction to the Approximation of Functions,” Dover, New York, 1981.

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  6. Scherer, R. and Zeller, K., Gestufte Approximation in zwei Variablen, in “Numerical Methods of Approximation Theory” Vol. 5 (L. Collatz, et al, Eds.), pp. 282–288, Birkhäuser Verlag, Basel, 1980.

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  7. Weinstein, S.E., Approximation of functions of several variables: product Chebyshev approximations I, J. Approx. Theory (1969), pp. 433–447.

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© 1982 Birkhäuser Verlag Basel

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Angelos, J., Schmidt, D. (1982). Some Remarks on Product Approximations. In: Schempp, W., Zeller, K. (eds) Multivariate Approximation Theory II. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 61. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7189-1_1

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  • DOI: https://doi.org/10.1007/978-3-0348-7189-1_1

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-7191-4

  • Online ISBN: 978-3-0348-7189-1

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