A Matrix Method for Efficient Computation of Bernstein Coefficients

We propose a generalized method, called as the Matrix method, for computation of the coefficients of multivariate Bernstein polynomials. The proposed Matrix method involves only matrix operations such as multiplication, inverse, transpose and reshape. For a general box-like domain, the computational complexity of the proposed method is O(n) in contrast to O(n) for existing methods. We conduct numerical experiments to compute the Bernstein coefficients for eleven polynomial problems (with dimensions varying from three to seven) defined over a unit box domain as well as a general box domain, with the existing methods and the proposed Matrix method. A comparison of the results shows the proposed algorithm to yield significant reductions in computational time for ‘larger’ number of Bernstein coefficients.