A higher order Sobolev-type inner product for orthogonal polynomials in several variables
We consider polynomials in several variables orthogonal with respect to a Sobolev-type inner product, obtained from adding a higher order gradient evaluated in a fixed point to a standard inner product. An expression for these polynomials in terms of the orthogonal family associated with the standar...
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| Veröffentlicht in: | Numerical algorithms 2015-01, Vol.68 (1), p.35-46 |
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| container_title | Numerical algorithms |
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| creator | Dueñas, Herbert Garza, Luis E. Piñar, Miguel |
| description | We consider polynomials in several variables orthogonal with respect to a Sobolev-type inner product, obtained from adding a higher order gradient evaluated in a fixed point to a standard inner product. An expression for these polynomials in terms of the orthogonal family associated with the standard inner product is obtained. A particular case using polynomials in the unit ball is analyzed, and some asymptotic results are derived. |
| doi_str_mv | 10.1007/s11075-014-9836-x |
| format | Article |
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| ispartof | Numerical algorithms, 2015-01, Vol.68 (1), p.35-46 |
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| subjects | Algebra Algorithms Asymptotic properties Computer Science Mathematical models Numeric Computing Numerical Analysis Original Paper Polynomials Theory of Computation |
| title | A higher order Sobolev-type inner product for orthogonal polynomials in several variables |
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