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

R. Hettich

Research output: Contribution to journalArticleAcademic

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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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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 -