Explicit formula relating the Jacobi, Hahn and Bernstein polynomials
SIAM Journal on Mathematical Analysis
Ten lectures on wavelets
Multivariable orthogonal polynomials and coupling coefficients for discrete series representations
SIAM Journal on Mathematical Analysis
Legendre-Bernstein basis transformations
Journal of Computational and Applied Mathematics - Special issue/Dedicated to Prof. Larry L. Schumaker on the occasion of his 60th birthday
Construction of orthogonal bases for polynomials in Bernstein form on triangular and simplex domains
Computer Aided Geometric Design
Monomial orthogonal polynomials of several variables
Journal of Approximation Theory
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Here, we give a simple proof of a new representation for orthogonal polynomials over triangular domains which overcomes the need to make symmetry destroying choices to obtain an orthogonal basis for polynomials of fixed degree by employing redundancy. A formula valid for simplices with Jacobi weights is given, and we exhibit its symmetries by using the Bernstein-Bezier form. From it, we obtain the matrix representing the orthogonal projection onto the space of orthogonal polynomials of fixed degree with respect to the Bernstein basis. The entries of this projection matrix are given explicitly by a multivariate analogue of the F23 hypergeometric function. Along the way we show that a polynomial is a Jacobi polynomial if and only if its Bernstein basis coefficients are a Hahn polynomial. We then discuss the application of these results to surface smoothing problems under linear constraints.