Communications of the ACM - Special issue on parallelism
Algorithms for computer algebra
Algorithms for computer algebra
Linear recurring sequences for computing the resultant of multivariate polynomials
SPOA VII Proceedings of the seventh Spanish symposium on Orthogonal polynomials and applications
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
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
Exploiting the Power of GPUs for Asymmetric Cryptography
CHES '08 Proceeding sof the 10th international workshop on Cryptographic Hardware and Embedded Systems
Efficient Acceleration of Asymmetric Cryptography on Graphics Hardware
AFRICACRYPT '09 Proceedings of the 2nd International Conference on Cryptology in Africa: Progress in Cryptology
Efficient Multiplication of Polynomials on Graphics Hardware
APPT '09 Proceedings of the 8th International Symposium on Advanced Parallel Processing Technologies
A complete modular resultant algorithm targeted for realization on graphics hardware
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
Reliable and efficient geometric computing
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
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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In this paper we report on the recent progress in computing bivariate polynomial resultants on Graphics Processing Units (GPU) Given two polynomials in ℤ[x,y], our algorithm first maps the polynomials to a prime field Then, each modular image is processed individually The GPU evaluates the polynomials at a number of points and computes univariate modular resultants in parallel The remaining “combine” stage of the algorithm is executed sequentially on the host machine Porting this stage to the graphics hardware is an object of ongoing research Our algorithm is based on an efficient modular arithmetic from [1] With the theory of displacement structure we have been able to parallelize the resultant algorithm up to a very fine scale suitable for realization on the GPU Our benchmarks show a substantial speed-up over a host-based resultant algorithm [2] from CGAL (www.cgal.org).