Collocation by singular splines |
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Authors: | Tina Bosner Mladen Rogina |
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Affiliation: | (1) Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia |
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Abstract: | Splines determined by the kernel of the differential operator are known to be useful to solve the singular boundary value problems of the form . One of the most successful methods is the collocation method based on special Chebyshev splines. We investigate the construction of the associated B-splines based on knot-insertion algorithms for their evaluation, and their application in collocation at generalized Gaussian points. Specially, we show how to obtain these points as eigenvalues of a symmetric tridiagonal matrix of order k. This research was supported by Grant 037-1193086-2771, by the Ministry of science, education and sports of the Republic of Croatia. |
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Keywords: | Chebyshev theory Singular splines Knot insertion Generalized de Boor algorithm Collocation Generalized Gaussian points |
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