{"publication_status":"published","language":[{"iso":"eng"}],"page":"705-715","publication":"Proc. 14th Annual International Symposium on Algorithms and Computation (ISAAC'03)","type":"conference","date_updated":"2022-01-06T06:53:27Z","series_title":"Lecture Notes in Computer Science, vol 2906. Springer, Berlin, Heidelberg","doi":"10.1007/978-3-540-24587-2_72","author":[{"full_name":"Ziegler, Martin","last_name":"Ziegler","first_name":"Martin"}],"abstract":[{"text":"Fast algorithms for arithmetic on real or complex polynomials are well-known and have proven to be not only asymptotically efficient but also very practical. Based on FAST FOURIER TRANSFORM, they for instance multiply two polynomials of degree up to N or multi-evaluate one at N points simultaneously within quasi-linear time O(N polylog N). An extension to (and in fact the mere definition of) polynomials over fields R and C to the SKEW-field H of quaternions is promising but still missing. The present work proposes three approaches which in the commutative case coincide but for H turn out to differ, each one satisfying some desirable properties while lacking others. For each notion, we devise algorithms for according arithmetic; these are quasi-optimal in that their running times match lower complexity bounds up to polylogarithmic factors.","lang":"eng"}],"status":"public","year":"2003","citation":{"ama":"Ziegler M. Quasi-optimal Arithmetic for Quaternion Polynomials. In: <i>Proc. 14th Annual International Symposium on Algorithms and Computation (ISAAC’03)</i>. Lecture Notes in Computer Science, vol 2906. Springer, Berlin, Heidelberg. ; 2003:705-715. doi:<a href=\"https://doi.org/10.1007/978-3-540-24587-2_72\">10.1007/978-3-540-24587-2_72</a>","mla":"Ziegler, Martin. “Quasi-Optimal Arithmetic for Quaternion Polynomials.” <i>Proc. 14th Annual International Symposium on Algorithms and Computation (ISAAC’03)</i>, 2003, pp. 705–15, doi:<a href=\"https://doi.org/10.1007/978-3-540-24587-2_72\">10.1007/978-3-540-24587-2_72</a>.","bibtex":"@inproceedings{Ziegler_2003, series={Lecture Notes in Computer Science, vol 2906. Springer, Berlin, Heidelberg}, title={Quasi-optimal Arithmetic for Quaternion Polynomials}, DOI={<a href=\"https://doi.org/10.1007/978-3-540-24587-2_72\">10.1007/978-3-540-24587-2_72</a>}, booktitle={Proc. 14th Annual International Symposium on Algorithms and Computation (ISAAC’03)}, author={Ziegler, Martin}, year={2003}, pages={705–715}, collection={Lecture Notes in Computer Science, vol 2906. Springer, Berlin, Heidelberg} }","ieee":"M. Ziegler, “Quasi-optimal Arithmetic for Quaternion Polynomials,” in <i>Proc. 14th Annual International Symposium on Algorithms and Computation (ISAAC’03)</i>, 2003, pp. 705–715.","short":"M. Ziegler, in: Proc. 14th Annual International Symposium on Algorithms and Computation (ISAAC’03), 2003, pp. 705–715.","apa":"Ziegler, M. (2003). Quasi-optimal Arithmetic for Quaternion Polynomials. In <i>Proc. 14th Annual International Symposium on Algorithms and Computation (ISAAC’03)</i> (pp. 705–715). <a href=\"https://doi.org/10.1007/978-3-540-24587-2_72\">https://doi.org/10.1007/978-3-540-24587-2_72</a>","chicago":"Ziegler, Martin. “Quasi-Optimal Arithmetic for Quaternion Polynomials.” In <i>Proc. 14th Annual International Symposium on Algorithms and Computation (ISAAC’03)</i>, 705–15. Lecture Notes in Computer Science, Vol 2906. Springer, Berlin, Heidelberg, 2003. <a href=\"https://doi.org/10.1007/978-3-540-24587-2_72\">https://doi.org/10.1007/978-3-540-24587-2_72</a>."},"user_id":"15415","date_created":"2020-08-24T14:18:19Z","department":[{"_id":"63"}],"publication_identifier":{"isbn":["9783540206958","9783540245872"],"issn":["0302-9743","1611-3349"]},"_id":"18196","title":"Quasi-optimal Arithmetic for Quaternion Polynomials"}