Abstract
Let f be an element of C [o, 1] and {g 1 ,..., g n } a Markoff system in C [o, 1]. We consider the last set as a subspace of L [o, 1]. Due to a known theorem of D. Jackson there exists for every f in C[o, 1] a unique best L 1 -approximation in the sub-space sp{g 1 ,..., g n } spanned by {g 1 ,..., g n } in L 1 [o,1]. 1967, K. H. USOW [4] established an algorithm for the computation of such best approximations. However, Usow succeeded to prove the convergence of his algorithm only for conditions on f and on {g 1 ,..., g n } which are fairly restrictiv and difficult to verify.
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References
Achieser, N.I.: Vorlesungen über Approximationstheorie. Akademie Verlag Berlin 1967.
Jackson, D.: A general class of problems in approximation. Amer. J. Math. 46 (1924), 215–234.
Rice, J. R.: The approximation of functions I, linear theory. Addison-Wesley Publ., Reading, 1964.
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© 1975 Springer Basel AG
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Marti, J.T. (1975). A Method for the Numerical Computation of Best L 1 -Approximations of Continuous Functions. In: Collatz, L., Meinardu, G. (eds) Numerische Methoden der Approximationstheorie. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’analyse Numérique, vol 26. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5961-5_9
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DOI: https://doi.org/10.1007/978-3-0348-5961-5_9
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-5962-2
Online ISBN: 978-3-0348-5961-5
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