{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T04:28:07Z","timestamp":1750220887906,"version":"3.41.0"},"reference-count":16,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2019,9,18]],"date-time":"2019-09-18T00:00:00Z","timestamp":1568764800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2019,9,18]]},"abstract":"<jats:p>\n            It is well known that if the leading matrix of a linear ordinary differential or difference system is nonsingular, then the determinant of this matrix contains some useful information on solutions of the system. We investigate a kind of non-arithmetic complexity of known algorithms for transforming a matrix of scalar operators to an equivalent matrix which has non-singular frontal, or, leading matrix. In the algorithms under consideration, the differentiation in the differential case and the shift in the difference case play a significant role. We give some analysis of the complexity measured as the number of differentiations or, resp., shifts in the worst case. We not only offer estimates of the complexity written using the\n            <jats:italic>O<\/jats:italic>\n            -notation, but we also show that some estimates are sharp and can not be improved.\n          <\/jats:p>","DOI":"10.1145\/3363520.3363522","type":"journal-article","created":{"date-parts":[[2019,9,18]],"date-time":"2019-09-18T18:35:06Z","timestamp":1568831706000},"page":"23-30","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Row reduction process for matrices of scalar operators"],"prefix":"10.1145","volume":"53","author":[{"given":"Sergei A.","family":"Abramov","sequence":"first","affiliation":[{"name":"\"Computer Science and Control\" of the Russian Academy of Sciences;, Vavilova, Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Moulay A.","family":"Barkatou","sequence":"additional","affiliation":[{"name":"Universit\u00e9 de Limoges;, Limoges, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2019,9,18]]},"reference":[{"doi-asserted-by":"publisher","key":"e_1_2_1_1_1","DOI":"10.1080\/10236199908808199"},{"key":"e_1_2_1_2_1","volume-title":"On the Differential and Full Algebraic Complexities of Operator Matrices Transformations. CASC 2016","author":"Abramov S.A.","year":"2016","unstructured":"S.A. Abramov . On the Differential and Full Algebraic Complexities of Operator Matrices Transformations. CASC 2016 , LNCS 9890, Springer, Heidelberg, 1--14 , 2016 . S.A. Abramov. On the Differential and Full Algebraic Complexities of Operator Matrices Transformations. CASC 2016, LNCS 9890, Springer, Heidelberg, 1--14, 2016."},{"doi-asserted-by":"publisher","key":"e_1_2_1_3_1","DOI":"10.1134\/S0965542517120028"},{"doi-asserted-by":"publisher","key":"e_1_2_1_4_1","DOI":"10.1007\/978-3-319-02297-0_1"},{"doi-asserted-by":"publisher","key":"e_1_2_1_5_1","DOI":"10.1145\/384101.384102"},{"unstructured":"S.A. Abramov M. Bronstein. Linear algebra for skew-polynomial matrices. Rapport de Recherche INRIA RR-4420 March 2002 http:\/\/www.inria.fr\/RRRT\/RR-4420.html  S.A. Abramov M. Bronstein. Linear algebra for skew-polynomial matrices. Rapport de Recherche INRIA RR-4420 March 2002 http:\/\/www.inria.fr\/RRRT\/RR-4420.html","key":"e_1_2_1_6_1"},{"doi-asserted-by":"publisher","key":"e_1_2_1_7_1","DOI":"10.1134\/S0361768813020023"},{"doi-asserted-by":"publisher","key":"e_1_2_1_8_1","DOI":"10.1007\/978-3-319-99639-4_2"},{"doi-asserted-by":"publisher","key":"e_1_2_1_9_1","DOI":"10.1016\/j.jsc.2011.12.016"},{"doi-asserted-by":"publisher","key":"e_1_2_1_10_1","DOI":"10.1016\/j.jsc.2005.10.002"},{"doi-asserted-by":"publisher","key":"e_1_2_1_11_1","DOI":"10.1006\/jsco.1998.0224"},{"doi-asserted-by":"publisher","key":"e_1_2_1_12_1","DOI":"10.1016\/j.jalgebra.2012.11.033"},{"doi-asserted-by":"publisher","key":"e_1_2_1_13_1","DOI":"10.1145\/860854.860888"},{"doi-asserted-by":"publisher","key":"e_1_2_1_14_1","DOI":"10.1016\/j.aim.2015.12.021"},{"doi-asserted-by":"publisher","key":"e_1_2_1_15_1","DOI":"10.1145\/1008328.1008329"},{"doi-asserted-by":"publisher","key":"e_1_2_1_16_1","DOI":"10.1016\/S0747-7171(02)00139-6"}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3363520.3363522","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3363520.3363522","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T23:44:25Z","timestamp":1750203865000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3363520.3363522"}},"subtitle":["storing the intermediate results of row transformation"],"short-title":[],"issued":{"date-parts":[[2019,9,18]]},"references-count":16,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,9,18]]}},"alternative-id":["10.1145\/3363520.3363522"],"URL":"https:\/\/doi.org\/10.1145\/3363520.3363522","relation":{},"ISSN":["1932-2240"],"issn-type":[{"type":"print","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2019,9,18]]},"assertion":[{"value":"2019-09-18","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}