Least squares approximation by splines with free knots

DOI10.1007/BF01732610zbMath0847.65004OpenAlexW2024690006MaRDI QIDQ1904276

Hubert Schwetlick, Torsten Schütze

Publication date: 1 February 1996

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01732610

zbMATH Keywords

smoothingnoisy datanumerical examplesdata reductiondata fitting\(B\)-splinesnonlinear least squaresfree knots splinesknot removal strategiesrobust optimization algorithm

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Numerical smoothing, curve fitting (65D10) Approximation with constraints (41A29) Spline approximation (41A15)

Related Items (13)

Pseudo-inverses of difference matrices and their application to sparse signal approximation ⋮ Curve approximation by adaptive neighborhood simulated annealing and piecewise Bézier curves ⋮ Data approximation by \(L^1\) spline fits with free knots ⋮ Globally optimal univariate spline approximations ⋮ Least squares splines with free knots: Global optimization approach. ⋮ Constrained approximation by splines with free knots ⋮ Unnamed Item ⋮ Plateau Phenomenon in Gradient Descent Training of RELU Networks: Explanation, Quantification, and Avoidance ⋮ Border estimation of a two-dimensional uniform distribution if data are measured with additive error ⋮ Multilevel regularization of wavelet based fitting of scattered data -- some experiments ⋮ B-spline curve fitting with invasive weed optimization ⋮ Geometrically designed, variable knot regression splines ⋮ Knot selection for least-squares and penalized splines

Uses Software

• FITPACK

Cites Work

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• A Spline Least Squares Method for Numerical Parameter Estimation in Differential Equations
• Method of optimal variable-knot spline interpolation in the 2 discrete norm
• A variable projection method for solving separable nonlinear least squares problems
• Approximation to Data by Splines with Free Knots
• Efficient implementation of a variable projection algorithm for nonlinear least squares problems
• An algorithm for data reduction using splines with free knots
• The Differentiation of Pseudo-Inverses and Nonlinear Least Squares Problems Whose Variables Separate
• On Polya Frequency Function. III. The Positivity of Translation Determinants With an Application to the Interpolation Problem by Spline Curves

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