Abstract:We increase the scope of previous work on change of basis between finite bases of polynomials by defining ascending and descending bases and introducing three techniques for defining them from known ones.The minimum degrees of polynomials in an ascending basis can increase such as with bases of Bernstein and Zernike Radial polynomials. They have applications in computer-aided design and optics.We give coefficient functions for mappings from the monomials to descending bases of Bernstein polynomials, and ascend… Show more
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