Gram matrix of Bernstein basis: properties and applications

• Lizheng Lu ^[1]
  1. [1] Zhejiang Gongshang University

     Zhejiang Gongshang University

     China

     
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 280, Nº 1 (15 May 2015), 2015, págs. 37-41
• Idioma: inglés
• DOI: 10.1016/j.cam.2014.11.037
• Texto completo no disponible (Saber más ...)
• Resumen

  • This note presents explicit expressions for the inverses of the Gram matrix of the Bernstein basis and its principal submatrices, by taking the advantages of the transformations between the Bernstein basis and the constrained dual Bernstein basis. Using the symmetry property, fast calculation of these matrices and their inverses is achieved. Significant improvements are obtained for applications including polynomial approximation of functions and degree reduction of Bézier curves.