A Modified Matrix Method for Efficient Computation of Bernstein Coefficients and Its GPU Parallelization

The Matrix Method (MM) [16] is an efficient method for computation of Bernstein coefficients (BCs) of a multivariate polynomial on a box-like domain. However, MM uses matrix transpose and reshape operations, which is time consuming for large matrices. The same operations are also costly in terms of energy for physical data movement in the computer memory [5]. In this paper, we propose the so-called Modified Matrix Method (MMM) which eliminates the matrix transpose and reshape operations in MM along with the associated data movements. We present two versions of MMM: the serial implementation and then the GPU (Graphics Processing Unit) [12], [15] parallel implementation. We then compare the performances of the proposed MMM versions versus MM on a set of multivariate polynomial test problems taken from the literature. On the test problems, we find that the proposed GPU parallel MMM implementation runs up to 27 times faster and gives up to 93% reduction in computing time over MM, on a TESLA K40. Thus, we suggest the GPU version of MMM for faster and more efficient computation of BCs of multivariate polynomials.