M.S. (Master of Science)
Department of Industrial and Systems Engineering
The past two decades have seen the development of L1 splines for interpolation and approximation of geometric data. L1 splines have been shown to preserve shapes better than the conventional L2 splines, especially for data with abrupt changes in the magnitude of spacing. Efficient computation plays an important role in the practical application of L1 splines. This thesis creates new computational methods for constructing bicubic L1 interpolating splines and bicubic L1 spline fits. The bicubic splines in this study are piecewise bicubic polynomials defined on a rectangular grid generated by the tensor product of nodes. We developed a hybrid computational method for bicubic L1 interpolating splines that calculates the first-order partial derivatives at the nodes by the univariate 5-point window algorithm and computes the cross partial derivatives by solving an optimization problem. For bicubic L1 splines fits, the existing gradient search method is made significantly more efficient by utilizing the local relation between data points and spline nodes. Further, domain decomposition method is used for computation on larger grids.
Rai, Priyesh Koyu, "Computational Methods For Bicubic L1 Splines" (2019). Graduate Research Theses & Dissertations. 7578.
Northern Illinois University
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