Orthogonal Polynomials on Planar Cubic Curves
Orthogonal polynomials in two variables on cubic curves are considered. For an integral with respect to an appropriate weight function defined on a cubic curve, an explicit basis of orthogonal polynomials is constructed in terms of two families of orthogonal polynomials in one variable. We show that...
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| Veröffentlicht in: | Foundations of computational mathematics 2023-02, Vol.23 (1), p.1-31 |
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| container_title | Foundations of computational mathematics |
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| creator | Fasondini, Marco Olver, Sheehan Xu, Yuan |
| description | Orthogonal polynomials in two variables on cubic curves are considered. For an integral with respect to an appropriate weight function defined on a cubic curve, an explicit basis of orthogonal polynomials is constructed in terms of two families of orthogonal polynomials in one variable. We show that these orthogonal polynomials can be used to approximate functions with cubic and square root singularities, and demonstrate their usage for solving differential equations with singular solutions. |
| doi_str_mv | 10.1007/s10208-021-09540-w |
| format | Article |
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| language | eng |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Applications of Mathematics Computer Science Differential equations Economics Functions, Orthogonal Linear and Multilinear Algebras Math Applications in Computer Science Mathematical analysis Mathematical research Mathematics Mathematics and Statistics Matrix Theory Numerical Analysis Polynomials Singularity (mathematics) Weighting functions |
| title | Orthogonal Polynomials on Planar Cubic Curves |
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