Fast algorithms for Taylor shifts and certain difference equations
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Parallel Real Root Isolation Using the Descartes Method
HiPC '99 Proceedings of the 6th International Conference on High Performance Computing
Parallel Real Root Isolation Using the Coefficient Sign Variation Method
Proceedings of the Second International Workshop on Computer Algebra and Parallelism
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
I/O complexity: The red-blue pebble game
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Polynomial real root isolation using Descarte's rule of signs
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Architecture-aware classical Taylor shift by 1
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
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Isolating the real roots of a univariate polynomial is a driving subject in computer algebra. This problem has been studied under various angles from algebraic algorithms [1, 2, 7] to implementation techniques [3, 5]. Today, multicores are the most popular parallel hardware architectures. Beside, understanding the implications of hierarchical memory on performance software engineering has become essential. These observations motivate our study. We analyze the cache complexity of the core routine of many real root isolation algorithms namely, the Taylor shift. Then, we present efficient multithreaded implementation on multicores.