WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 23, 2024
Isogeometric Method for Least Squares Problem
Authors: , ,
Abstract: In the framework of this work, we used the isogeometric method to solve the least squares problem in one dimension, on a curve of $$\mathbb{R}^{d}, d = 1, 2$$, including a semicircle. For this purpose, we presented the isogeometric method and the tools necessary for the description of this method, namely, the b splines basis, the parameterization of the $$\mathbb{R}^{d}, d = 1, 2$$ curve. We formulated the least squares problem which is a minimization problem. This problem was solved by using the Discontinuous Galerkin (DG) and the b splines basis as the approximation basis. The numerical method was validated by evaluating the error. For this purpose, an inverse inequality was therefore used.
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Keywords: Isogeometric method, Least squares problem, B-spline basis, Parameterization, Discontinuous Galerkin, Inverse inequality
Pages: 750-756
DOI: 10.37394/23206.2024.23.78