Kriterien erster und zweiter Ordnung für lokal beste Approximationen bei Problemen mit Nebenbedingungen

R. Hettich

    Research output: Contribution to journalArticleAcademic

    3 Citations (Scopus)
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    Abstract

    In a previous paper [6] we considered the problem of approximating (in the Chebyshev-norm) a real-valued functionf(x) on a compact subsetX<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 were derived. In this paper we generalize these results to problems where the setP of admitted parameters is constrained by some inequality. Included are subjects as monotone, one-sided or restricted range approximation.
    Original languageUndefined
    Pages (from-to)109-122
    JournalNumerische Mathematik
    Volume25
    Issue number1
    DOIs
    Publication statusPublished - 1975

    Keywords

    • IR-85472

    Cite this

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    title = "Kriterien erster und zweiter Ordnung f{\"u}r lokal beste Approximationen bei Problemen mit Nebenbedingungen",
    abstract = "In a previous paper [6] we considered the problem of approximating (in the Chebyshev-norm) a real-valued functionf(x) on a compact subsetX<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 were derived. In this paper we generalize these results to problems where the setP of admitted parameters is constrained by some inequality. Included are subjects as monotone, one-sided or restricted range approximation.",
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    author = "R. Hettich",
    year = "1975",
    doi = "10.1007/BF01419533",
    language = "Undefined",
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    pages = "109--122",
    journal = "Numerische Mathematik",
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    Kriterien erster und zweiter Ordnung für lokal beste Approximationen bei Problemen mit Nebenbedingungen. / Hettich, R.

    In: Numerische Mathematik, Vol. 25, No. 1, 1975, p. 109-122.

    Research output: Contribution to journalArticleAcademic

    TY - JOUR

    T1 - Kriterien erster und zweiter Ordnung für lokal beste Approximationen bei Problemen mit Nebenbedingungen

    AU - Hettich, R.

    PY - 1975

    Y1 - 1975

    N2 - In a previous paper [6] we considered the problem of approximating (in the Chebyshev-norm) a real-valued functionf(x) on a compact subsetX<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 were derived. In this paper we generalize these results to problems where the setP of admitted parameters is constrained by some inequality. Included are subjects as monotone, one-sided or restricted range approximation.

    AB - In a previous paper [6] we considered the problem of approximating (in the Chebyshev-norm) a real-valued functionf(x) on a compact subsetX<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 were derived. In this paper we generalize these results to problems where the setP of admitted parameters is constrained by some inequality. Included are subjects as monotone, one-sided or restricted range approximation.

    KW - IR-85472

    U2 - 10.1007/BF01419533

    DO - 10.1007/BF01419533

    M3 - Article

    VL - 25

    SP - 109

    EP - 122

    JO - Numerische Mathematik

    JF - Numerische Mathematik

    SN - 0029-599X

    IS - 1

    ER -