{"paper":{"title":"B\\'ezier form of dual bivariate Bernstein polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Pawe{\\l} Keller, Pawe{\\l} Wo\\'zny, Stanis{\\l}aw Lewanowicz","submitted_at":"2015-10-28T10:09:10Z","abstract_excerpt":"Dual Bernstein polynomials of one or two variables have proved to be very useful in obtaining B\\'{e}zier form of the $L^2$-solution of the problem of best polynomial approximation of B\\'{e}zier curve or surface. In this connection, the B\\'{e}zier coefficients of dual Bernstein polynomials are to be evaluated at a reasonable cost. In this paper, a set of recurrence relations satisfied by the B\\'{e}zier coefficients of dual bivariate Bernstein polynomials is derived and an efficient algorithm for evaluation of these coefficients is proposed. Applications of this result to some approximation prob"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08246","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}