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Shape-preserving, multiscale fitting of univariate data by cubic L1 smoothing splines

โœ Scribed by John E. Lavery

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

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โœฆ Synopsis

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 smoothing splines preserve shape well for arbitrary data, including multiscale data with abrupt changes in magnitude and spacing. Extensions to higher-degree and higher-dimensional smoothing splines are outlined.

๐Ÿ“œ SIMILAR VOLUMES

Univariate cubic Lp splines and shape-pr
Univariate cubic Lp splines and shape-preserving, multiscale interpolation by univariate cubic L1 splines
โœ John E. Lavery ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 180 KB

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, cub