Gram matrix of Bernstein basis: Properties and applications

作者：Lu, Lizheng^*

来源：Journal of Computational and Applied Mathematics, 2015, 280: 37-41.

DOI：10.1016/j.cam.2014.11.037

• Gram matrix
• Bernstein basis
• Constrained dual Bernstein basis
• Fast calculation
• Approximation

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 Bezier curves.

• 出版日期2015-5-15
• 单位浙江工商大学