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- W2051244235 abstract "In the present paper the interpolation of data sets is considered under two-sided constraints on the derivatives. Thus, e.g., the interpolants may be convex on some pieces of the domain and concave on others. For solving these interpolation problems quadratic and cubic splines are used. In extending earlier results necessary and sufficient existence conditions are derived as well as numerical procedures for determining interpolants with minimal curvature. In den letzten Jahren ist die Interpolation von Datenmengen verstärkt unter Beachtung von Nebenbedingungen betrachtet worden. Hierzu gehört z. B. die konvexe Interpolation, welche durch die Nichtnegativität der zweiten Ableitung charakterisiert ist. In der vorliegenden Arbeit wird nun die Interpolation unter zweiseitigen Einschränkungen für die Ableitungen untersucht. Auf diese Weise kann z. B. erfaßt werden, daß die Interpolierende auf gewissen Teilintervallen konvex und auf anderen konkav sein soll. Zur Interpolation werden sowohl quadratische als auch kubische Splines verwendet. In Verallgemeinerung früherer Ergebnisse werden vor allem hinreichende und notwendige Existenzaussagen hergeleitet sowie Möglichkeiten zur effektiven numerischen Ermittlung von Spline-Interpolierenden aufgezeigt, deren Krümmung unter den jetzigen Nebenbedingungen minimal ist." @default.
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- W2051244235 date "1989-01-01" @default.
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- W2051244235 title "Spline Interpolation under Two-Sided Restrictions on the Derivatives" @default.
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- W2051244235 doi "https://doi.org/10.1002/zamm.19890691012" @default.
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