Multivariate polynomial approximation in the hypercube
A theorem is proved concerning approximation of analytic functions by multivariate polynomials in the s-dimensional hypercube. The geometric convergence rate is determined not by the usual notion of degree of a multivariate polynomial, but by the Euclidean degree, defined in terms of the 2-norm rath...
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| Format: | Journal article |
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American Mathematical Society
2017
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| _version_ | 1797060129665843200 |
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| author | Trefethen, L |
| author_facet | Trefethen, L |
| author_sort | Trefethen, L |
| collection | OXFORD |
| description | A theorem is proved concerning approximation of analytic functions by multivariate polynomials in the s-dimensional hypercube. The geometric convergence rate is determined not by the usual notion of degree of a multivariate polynomial, but by the Euclidean degree, defined in terms of the 2-norm rather than the 1-norm of the exponent vector k of a monomial $x_1^{k_1}\cdots \kern .8pt x_s^{k_s}$. |
| first_indexed | 2024-03-06T20:13:12Z |
| format | Journal article |
| id | oxford-uuid:2b479033-64e3-4096-89e8-6b26d038f331 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T20:13:12Z |
| publishDate | 2017 |
| publisher | American Mathematical Society |
| record_format | dspace |
| spelling | oxford-uuid:2b479033-64e3-4096-89e8-6b26d038f3312022-03-26T12:29:57ZMultivariate polynomial approximation in the hypercubeJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:2b479033-64e3-4096-89e8-6b26d038f331*subject*Symplectic Elements at OxfordAmerican Mathematical Society2017Trefethen, LA theorem is proved concerning approximation of analytic functions by multivariate polynomials in the s-dimensional hypercube. The geometric convergence rate is determined not by the usual notion of degree of a multivariate polynomial, but by the Euclidean degree, defined in terms of the 2-norm rather than the 1-norm of the exponent vector k of a monomial $x_1^{k_1}\cdots \kern .8pt x_s^{k_s}$. |
| spellingShingle | *subject* Trefethen, L Multivariate polynomial approximation in the hypercube |
| title | Multivariate polynomial approximation in the hypercube |
| title_full | Multivariate polynomial approximation in the hypercube |
| title_fullStr | Multivariate polynomial approximation in the hypercube |
| title_full_unstemmed | Multivariate polynomial approximation in the hypercube |
| title_short | Multivariate polynomial approximation in the hypercube |
| title_sort | multivariate polynomial approximation in the hypercube |
| topic | *subject* |
| work_keys_str_mv | AT trefethenl multivariatepolynomialapproximationinthehypercube |