Optimized Multivariate Polynomial Determinant on GPU (2010.12117v1)

Abstract: We present an optimized algorithm calculating determinant for multivariate polynomial matrix on GPU. The novel algorithm provides precise determinant for input multivariate polynomial matrix in controllable time. Our approach is based on modular methods and split into Fast Fourier Transformation, Condensation method and Chinese Remainder Theorem where each algorithm is paralleled on GPU. The experiment results show that our parallel method owns substantial speedups compared to Maple, allowing memory overhead and time expedition in steady increment. We are also able to deal with complex matrix which is over the threshold on Maple and constrained on CPU. In addition, calculation during the process could be recovered without losing accuracy at any point regardless of disruptions. Furthermore, we propose a time prediction for calculation of polynomial determinant according to some basic matrix attributes and we solve an open problem relating to harmonic elimination equations on the basis of our GPU implementation.