Algorithms for computer algebra
Algorithms for computer algebra
Displacement structure: theory and applications
SIAM Review
A Fast Stable Solver for Nonsymmetric Toeplitz and Quasi-Toeplitz Systems of Linear Equations
SIAM Journal on Matrix Analysis and Applications
The Montgomery Modular Inverse-Revisited
IEEE Transactions on Computers - Special issue on computer arithmetic
Distributed Symbolic Computation with DTS
IRREGULAR '95 Proceedings of the Second International Workshop on Parallel Algorithms for Irregularly Structured Problems
Parallel Computation of Modular Multivariate Polynominal Resultants on a Shared Memory Machine
CONPAR 94 - VAPP VI Proceedings of the Third Joint International Conference on Vector and Parallel Processing: Parallel Processing
A New Approach to Resultant Computations and Other Algorithms with Exact Division
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
The calculation of multivariate polynomial resultants
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
Probabilistic algorithms for computing resultants
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Efficient parallel factorization and solution of structured and unstructured linear systems
Journal of Computer and System Sciences
Modular resultant algorithm for graphics processors
ICA3PP'10 Proceedings of the 10th international conference on Algorithms and Architectures for Parallel Processing - Volume Part I
Reliable and efficient geometric computing
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Solving bivariate polynomial systems on a GPU
ACM Communications in Computer Algebra
Arrangement computation for planar algebraic curves
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Computing resultants on Graphics Processing Units: Towards GPU-accelerated computer algebra
Journal of Parallel and Distributed Computing
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This paper presents a complete modular approach to computing bivariate polynomial resultants on Graphics Processing Units (GPU). Given two polynomials, the algorithm first maps them to a prime field for sufficiently many primes, and then processes each modular image individually. We evaluate each polynomial at several points and compute a set of univariate resultants for each prime in parallel on the GPU. The remaining "combine" stage of the algorithm comprising polynomial interpolation and Chinese remaindering is also executed on the graphics processor. The GPU algorithm returns coefficients of the resultant as a set of Mixed Radix (MR) digits. Finally, the large integer coefficients are recovered from the MR representation on the host machine. With the approach of displacement structure [16] and efficient modular arithmetic [8] we have been able to achieve more than 100x speed-up over a CPU-based resultant algorithm from Maple 13.