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- W4242505667 abstract "This paper is concerned with the problem of existence of monotone and/or convex splines, having degree <italic>n</italic> and order of continuity <italic>k</italic>, which interpolate to a set of data at the knots. The interpolating splines are obtained by using Bernstein polynomials of suitable continuous piecewise linear functions; they satisfy the inequality <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=k less-than-or-slanted-equals n minus k> <mml:semantics> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>⩽<!-- ⩽ --></mml:mo> <mml:mi>n</mml:mi> <mml:mo>−<!-- − --></mml:mo> <mml:mi>k</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>k leqslant n - k</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. The theorems presented here are useful in developing algorithms for the construction of shape-preserving splines interpolating arbitrary sets of data points. Earlier results of McAllister, Passow and Roulier can be deduced from those given in this paper." @default.
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- W4242505667 date "1986-01-01" @default.
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- W4242505667 title "On monotone and convex spline interpolation" @default.
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- W4242505667 doi "https://doi.org/10.1090/s0025-5718-1986-0815841-7" @default.
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