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Univariate cubic Lp splines and shape-preserving, multiscale interpolation by univariate cubic L1 splines

โœ Scribed by John E. Lavery

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
180 KB
Volume
17
Category
Article
ISSN
0167-8396

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โœฆ Synopsis

Univariate cubic L p interpolating splines, 1 p โˆž, defined by minimizing the L p norm of the second derivative over a finite-dimensional spline space, are introduced. Cubic L 2 splines, which coincide with conventional cubic splines, and cubic L โˆž splines do not preserve shape well. In contrast, cubic L 1 splines provide C 1 -smooth, shape-preserving, multiscale interpolation of arbitrary data, including data with abrupt changes in spacing and magnitude, with no need for monotonicity or convexity constraints, node adjustment or other user input. Extensions to higher-degree and higherdimensional L 1 splines are outlined. Cubic L 1 splines are particularly useful in modeling terrain, geophysical features, biological objects and financial processes.

๐Ÿ“œ SIMILAR VOLUMES

Shape-preserving, multiscale fitting of
Shape-preserving, multiscale fitting of univariate data by cubic L1 smoothing splines
โœ John E. Lavery ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 161 KB

A new class of C 1 -smooth univariate cubic L 1 smoothing splines is introduced. The coefficients of these smoothing splines are calculated by minimizing the weighted sum of the 1 norm of the residuals of the data-fitting equations and the L 1 norm of the second derivative of the spline. Cubic L 1 s