A Matrix Method for Efficient Computation of Bernstein Coefficients
Shashwati Ray, P. S. V. Nataraj · 2012
We propose a generalized method, called as the Matrix method, for computationofthecoefficientsofmultivariateBernsteinpolynomials. 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 l+1) in contrast to O(n 2l) 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.