Curve and surface fitting with splines
Curve and surface fitting with splines
Linear optimization and extensions: theory and algorithms
Linear optimization and extensions: theory and algorithms
Fitting Monotone Surfaces to Scattered Data Using C1 Piecewise Cubics
SIAM Journal on Numerical Analysis
Computer Aided Geometric Design
Shape-preserving, multiscale fitting of univariate data by cubic L1 smoothing splines
Computer Aided Geometric Design
An Efficient Algorithm for Generating Univariate Cubic L1 Splines
Computational Optimization and Applications
Shape-preserving properties of univariate cubic L1 splines
Journal of Computational and Applied Mathematics
Shape-preserving, multiscale interpolation by bi- and multivariate cubic L1 splines
Computer Aided Geometric Design
A compressed primal-dual method for generating bivariate cubic L1 splines
Journal of Computational and Applied Mathematics
Fast L1kCk polynomial spline interpolation algorithm with shape-preserving properties
Computer Aided Geometric Design
Surface Reconstruction and Image Enhancement via $L^1$-Minimization
SIAM Journal on Scientific Computing
Computational Optimization and Applications
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Bivariate cubic L"1 splines provide C^1-smooth, shape-preserving interpolation of arbitrary data, including data with abrupt changes in spacing and magnitude. The minimization principle for bivariate cubic L"1 splines results in a nondifferentiable convex optimization problem. This problem is reformulated as a generalized geometric programming problem. A geometric dual with a linear objective function and convex cubic constraints is derived. A linear system for dual-to-primal conversion is established. The results of computational experiments are presented.