[{"user_id":"15415","abstract":[{"lang":"eng"}],"date_created":"2020-08-24T14:18:19Z","status":"public","publication":"Proc. 14th Annual International Symposium on Algorithms and Computation (ISAAC'03)","author":[{"last_name":"Ziegler","first_name":"Martin"}],"_id":"18196","uri_base":"https://ris.uni-paderborn.de","page":"705-715","citation":{"chicago":"Ziegler, Martin. “Quasi-Optimal Arithmetic for Quaternion Polynomials.” In Proc. 14th Annual International Symposium on Algorithms and Computation (ISAAC’03), 705–15. Lecture Notes in Computer Science, Vol 2906. Springer, Berlin, Heidelberg, 2003. https://doi.org/10.1007/978-3-540-24587-2_72.","apa":"Ziegler, M. (2003). Quasi-optimal Arithmetic for Quaternion Polynomials. In Proc. 14th Annual International Symposium on Algorithms and Computation (ISAAC’03) (pp. 705–715). https://doi.org/10.1007/978-3-540-24587-2_72","bibtex":"@inproceedings{Ziegler_2003, series={Lecture Notes in Computer Science, vol 2906. Springer, Berlin, Heidelberg}, title={Quasi-optimal Arithmetic for Quaternion Polynomials}, DOI={10.1007/978-3-540-24587-2_72}, 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} }","mla":"Ziegler, Martin. “Quasi-Optimal Arithmetic for Quaternion Polynomials.” Proc. 14th Annual International Symposium on Algorithms and Computation (ISAAC’03), 2003, pp. 705–15, doi:10.1007/978-3-540-24587-2_72.","short":"M. Ziegler, in: Proc. 14th Annual International Symposium on Algorithms and Computation (ISAAC’03), 2003, pp. 705–715.","ieee":"M. Ziegler, “Quasi-optimal Arithmetic for Quaternion Polynomials,” in Proc. 14th Annual International Symposium on Algorithms and Computation (ISAAC’03), 2003, pp. 705–715."},"type":"conference","dc":{"title":["Quasi-optimal Arithmetic for Quaternion Polynomials"],"creator":["Ziegler, Martin"],"source":["Ziegler M. Quasi-optimal Arithmetic for Quaternion Polynomials. In: Proc. 14th Annual International Symposium on Algorithms and Computation (ISAAC’03). Lecture Notes in Computer Science, vol 2906. Springer, Berlin, Heidelberg. ; 2003:705-715. doi:10.1007/978-3-540-24587-2_72"],"identifier":["https://ris.uni-paderborn.de/record/18196"],"relation":["info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-540-24587-2_72","info:eu-repo/semantics/altIdentifier/issn/0302-9743","info:eu-repo/semantics/altIdentifier/issn/1611-3349","info:eu-repo/semantics/altIdentifier/isbn/9783540206958","info:eu-repo/semantics/altIdentifier/isbn/9783540245872"],"description":["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."],"date":["2003"],"language":["eng"],"type":["info:eu-repo/semantics/conferenceObject","doc-type:conferenceObject","text","http://purl.org/coar/resource_type/c_5794"],"rights":["info:eu-repo/semantics/closedAccess"]},"dini_type":"doc-type:conferenceObject","publication_status":"published","publication_identifier":{"isbn":[],"issn":[]},"department":[{"tree":[{"_id":"7"},{"_id":"34"},{"_id":"44"},{"_id":"43"}],"_id":"63"}],"creator":{"id":"15415","login":"koala"},"date_updated":"2022-01-06T06:53:27Z","language":[{}],"series_title":"Lecture Notes in Computer Science, vol 2906. Springer, Berlin, Heidelberg"}]