{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,12,30]],"date-time":"2022-12-30T05:22:50Z","timestamp":1672377770728},"reference-count":14,"publisher":"Association for Computing Machinery (ACM)","issue":"1","content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["SIGSAM Bull."],"published-print":{"date-parts":[[1994,3]]},"abstract":"\n Factorization and testing for irreducibility has turned out to be one of the most important algorithms for handling linear ode's. The main hindrance for applying it is its tremendeous complexity originating to a large extent from solving certain Riccati equations which occur during the factorization. The solution procedure for these Riccati equations is much more manageable if it is subdivided into two major parts. At first so called\n solution candidates<\/jats:italic>\n are determined each of which depends only on the parameters of a single irreducible denominator or the behavior at infinity. In a second step it is tried to complete each candidate into a genuine solution of the Riccati equation, possibly including an unspecified number of additional first order poles. Furthermore a scheme is proposed for running the factorization procedure in parallel on a two-processor machine in which possible factors are searched for both from the right and the left at the same time.\n <\/jats:p>","DOI":"10.1145\/182130.182132","type":"journal-article","created":{"date-parts":[[2007,1,17]],"date-time":"2007-01-17T18:32:02Z","timestamp":1169058722000},"page":"9-17","update-policy":"http:\/\/dx.doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Efficient factorization of linear ODE's"],"prefix":"10.1145","volume":"28","author":[{"given":"Fritz","family":"Schwarz","sequence":"first","affiliation":[]}],"member":"320","published-online":{"date-parts":[[1994,3]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/74540.74544"},{"key":"e_1_2_1_2_1","first-page":"236","volume":"76","author":"Frobenius G.","year":"1873","journal-title":"Mathematik"},{"key":"e_1_2_1_3_1","volume-title":"Teubner","author":"Schlesinger L.","year":"1968"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01446541"},{"key":"e_1_2_1_5_1","first-page":"115","volume":"124","author":"Landau E.","year":"1902","journal-title":"Mathematik"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1993.1032"},{"key":"e_1_2_1_7_1","unstructured":"F. Schwarz Rational Solutions of Riccati Equations to appear. F. Schwarz Rational Solutions of Riccati Equations to appear."},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.2307\/2374045"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/143242.143264"},{"key":"e_1_2_1_10_1","volume-title":"CATHODE Meeting, Schloß Dagstuhl","author":"Singer M.","year":"1992"},{"key":"e_1_2_1_11_1","unstructured":"M. Bronstein On Solutions of Linear Ordinary Differential Equations in their Coefficient Field. M. Bronstein On Solutions of Linear Ordinary Differential Equations in their Coefficient Field."},{"key":"e_1_2_1_12_1","unstructured":"S. Abramov Rational Solutions of Linear Differential and Difference Equations with Polynomial Coefficients. S. Abramov Rational Solutions of Linear Differential and Difference Equations with Polynomial Coefficients."},{"key":"e_1_2_1_13_1","volume-title":"Teubner","author":"L.","year":"1882"},{"key":"e_1_2_1_14_1","unstructured":"F. Schwarz LODES: Linear Ordinary Differential Equation Solver User Manual. F. Schwarz LODES: Linear Ordinary Differential Equation Solver User Manual."}],"container-title":["ACM SIGSAM Bulletin"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/182130.182132","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,29]],"date-time":"2022-12-29T19:14:56Z","timestamp":1672341296000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/182130.182132"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,3]]},"references-count":14,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1994,3]]}},"alternative-id":["10.1145\/182130.182132"],"URL":"https:\/\/doi.org\/10.1145\/182130.182132","relation":{},"ISSN":["0163-5824"],"issn-type":[{"value":"0163-5824","type":"print"}],"subject":[],"published":{"date-parts":[[1994,3]]},"assertion":[{"value":"1994-03-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}