Kriterien zweiter Ordnung für lokal beste Approximationen

R. Hettich

    Research output: Contribution to journalArticleAcademic

    5 Citations (Scopus)
    22 Downloads (Pure)

    Abstract

    Consider the problem of approximating (in the Chebyshev-norm) a real-valued functionf(x) on a compact subsetX of ℝm,m≧1, by an element of a set of functionsa(p, x), p∈P,P⊆ ℝn an open set. Both necessary and sufficient conditions of the second order for ana(p0,x) to be a locally best approximation are derived. Apart from conditions on the differentiability off anda, onX, and on the error functionf(x)−a(p0,x) we impose no restrictions on the problem. This makes the results applicable to a broad class of problems.
    Original languageUndefined
    Pages (from-to)409-417
    JournalNumerische Mathematik
    Volume22
    Issue number5
    DOIs
    Publication statusPublished - 1974

    Keywords

    • IR-85463

    Cite this

    Hettich, R. / Kriterien zweiter Ordnung für lokal beste Approximationen. In: Numerische Mathematik. 1974 ; Vol. 22, No. 5. pp. 409-417.
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    Kriterien zweiter Ordnung für lokal beste Approximationen. / Hettich, R.

    In: Numerische Mathematik, Vol. 22, No. 5, 1974, p. 409-417.

    Research output: Contribution to journalArticleAcademic

    TY - JOUR

    T1 - Kriterien zweiter Ordnung für lokal beste Approximationen

    AU - Hettich, R.

    PY - 1974

    Y1 - 1974

    N2 - Consider the problem of approximating (in the Chebyshev-norm) a real-valued functionf(x) on a compact subsetX of ℝm,m≧1, by an element of a set of functionsa(p, x), p∈P,P⊆ ℝn an open set. Both necessary and sufficient conditions of the second order for ana(p0,x) to be a locally best approximation are derived. Apart from conditions on the differentiability off anda, onX, and on the error functionf(x)−a(p0,x) we impose no restrictions on the problem. This makes the results applicable to a broad class of problems.

    AB - Consider the problem of approximating (in the Chebyshev-norm) a real-valued functionf(x) on a compact subsetX of ℝm,m≧1, by an element of a set of functionsa(p, x), p∈P,P⊆ ℝn an open set. Both necessary and sufficient conditions of the second order for ana(p0,x) to be a locally best approximation are derived. Apart from conditions on the differentiability off anda, onX, and on the error functionf(x)−a(p0,x) we impose no restrictions on the problem. This makes the results applicable to a broad class of problems.

    KW - IR-85463

    U2 - 10.1007/BF01436923

    DO - 10.1007/BF01436923

    M3 - Article

    VL - 22

    SP - 409

    EP - 417

    JO - Numerische Mathematik

    JF - Numerische Mathematik

    SN - 0029-599X

    IS - 5

    ER -