Uniform approximation of vector-valued functions with a constraint

Author:
Geneva G. Belford

Journal:
Math. Comp. **26** (1972), 487-492

MSC:
Primary 41A50

DOI:
https://doi.org/10.1090/S0025-5718-1972-0310511-6

MathSciNet review:
0310511

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Abstract: This paper deals with existence and characterization of best approximations to vector-valued functions. The approximations are themselves vector-valued functions with components taken from a linear space, but the constraint is imposed that certain of the approximation parameters should be identical for all components.

**[1]**C. B. Dunham, ``Simultaneous Chebyshev approximation of functions on an interval,''*Proc. Amer. Math. Soc.*, v. 18, 1967, pp. 472-477. MR**35**#3334. MR**0212463 (35:3334)****[2]**L. W. Johnson, ``Uniform approximation of vector-valued functions,''*Numer. Math.*, v. 13, 1969, pp. 238-244. MR**40**#610. MR**0247342 (40:610)****[3]**L. W. Johnson, ``Unicity in the uniform approximation of vector-valued functions,''*Bull. Austral. Math. Soc.*, v. 3, 1970, pp. 193-198. MR**0275038 (43:796)****[4]**G. Meinardus,*Approximation of Functions: Theory and Numerical Methods*, Springer Tracts in Natural Philosophy, vol. 13, Springer-Verlag, New York, 1967. MR**36**#571. MR**0217482 (36:571)****[5]**D. G. Moursund, ``Chebyshev approximations of a function and its derivatives,''*Math. Comp.*, v. 18, 1964, pp. 382-389. MR**29**#3804. MR**0166529 (29:3804)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1972-0310511-6

Keywords:
Uniform approximation,
vector-valued approximation,
linear approximation,
characterization of best approximation,
polynomial approximation

Article copyright:
© Copyright 1972
American Mathematical Society