Optimal Asynchronous Newton Method for the Solution of Nonlinear Equations
Journal of the ACM (JACM)
USSR Computational Mathematics and Mathematical Physics
A fast parallel algorithm for determining all roots of a polynomial with real roots
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Some parallel methods for polynomial root-finding
Journal of Computational and Applied Mathematics - The 11th South African Symposium on Numerical Mathematics
A study on the new Muller's method
Publications of the Research Institute for Mathematical Sciences
Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
A Highly Parallel Algorithm for Root Extraction
IEEE Transactions on Computers
Optimum Broadcasting and Personalized Communication in Hypercubes
IEEE Transactions on Computers
Parallel polynomial computations by recursive processes
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Specified precision polynomial root isolation is in NC
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
Asynchronous Iterative Methods for Multiprocessors
Journal of the ACM (JACM)
A highly parallel algorithm for approximating all zeros of a polynomial with only real zeros
Communications of the ACM
A modified Newton method for polynomials
Communications of the ACM
Big Omicron and big Omega and big Theta
ACM SIGACT News
Iterative Algorithms on Heterogeneous Network Computing: Parallel Polynomial Root Extracting
HiPC '02 Proceedings of the 9th International Conference on High Performance Computing
Family of simultaneous methods of Hansen-Patrick's type
Applied Numerical Mathematics
Parallel Polynomial Root Extraction on A Ring of Processors
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Workshop 15 - Volume 16
A posteriori error bound methods for the inclusion of polynomial zeros
Journal of Computational and Applied Mathematics
A family of root-finding methods with accelerated convergence
Computers & Mathematics with Applications
Impact of asynchronism on GPU accelerated parallel iterative computations
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume Part I
Hi-index | 0.01 |
We have studied various implementations of iterative polynomial root finding methods on a distributed memory multicomputer. These methods are based on the construction of a sequence of approximations that converge to the set of zeros. The synchronous version consists in sharing the computation of the next iterate among the processors and updating their data through a total exchange of their results. In order to decrease thecommunication cost, we introduce asynchronous versions. The computation of the nextiterate is still shared among the processor, but the updating is done by using only nearestneighbor communications. We prove that under weak conditions, these asynchronousversions are still locally convergent, even if their convergence orders are reduced. Weanalyze the behavior of the asynchronous methods in function of their delay, thetopology of the interconnection network, and the elementary computation andcommunication times. We have implemented and compared these methods on ahypercube multicomputer.