{"_id":"ixZ3Ekx5XoxXAXnpD","bibbaseid":"dureisseix-generalizedfractionfreelufactorizationforsingularsystemswithkernelextraction-2012","authorIDs":[],"author_short":["Dureisseix, D."],"bibdata":{"bibtype":"article","type":"article","title":"Generalized fraction-free LU factorization for singular systems with kernel extraction","volume":"436","issn":"0024-3795","url":"http://www.sciencedirect.com/science/article/pii/S0024379511004617","doi":"10.1016/j.laa.2011.06.013","abstract":"Linear systems are usually solved with Gaussian elimination. Especially when multiple right hand sides are involved, an efficient procedure is to provide a factorization of the left hand side. When exact computations are required in an integral domain, complete fraction-free factorization and forward–backward substitutions are useful. This article deals with the case where the left hand side may be singular. In such a case, kernels are required to test a solvability condition and to derive the general form of the solutions. The complete fraction-free algorithms are therefore extended to deal with singular systems and to provide the kernels with exact computations on the same integral domain where the initial data take their entries.","number":"1","urldate":"2016-05-05","journal":"Linear Algebra and its Applications","author":[{"propositions":[],"lastnames":["Dureisseix"],"firstnames":["David"],"suffixes":[]}],"month":"January","year":"2012","keywords":"CFFLU, Exact factorization, Gaussian elimination, Integral domain, Linear system, mathematics, research, symbolic computation, uses sympy","pages":"27–40","bibtex":"@article{dureisseix_generalized_2012,\n\ttitle = {Generalized fraction-free {LU} factorization for singular systems with kernel extraction},\n\tvolume = {436},\n\tissn = {0024-3795},\n\turl = {http://www.sciencedirect.com/science/article/pii/S0024379511004617},\n\tdoi = {10.1016/j.laa.2011.06.013},\n\tabstract = {Linear systems are usually solved with Gaussian elimination. Especially when multiple right hand sides are involved, an efficient procedure is to provide a factorization of the left hand side. When exact computations are required in an integral domain, complete fraction-free factorization and forward–backward substitutions are useful. This article deals with the case where the left hand side may be singular. In such a case, kernels are required to test a solvability condition and to derive the general form of the solutions. The complete fraction-free algorithms are therefore extended to deal with singular systems and to provide the kernels with exact computations on the same integral domain where the initial data take their entries.},\n\tnumber = {1},\n\turldate = {2016-05-05},\n\tjournal = {Linear Algebra and its Applications},\n\tauthor = {Dureisseix, David},\n\tmonth = jan,\n\tyear = {2012},\n\tkeywords = {CFFLU, Exact factorization, Gaussian elimination, Integral domain, Linear system, mathematics, research, symbolic computation, uses sympy},\n\tpages = {27--40},\n}\n\n","author_short":["Dureisseix, D."],"key":"dureisseix_generalized_2012","id":"dureisseix_generalized_2012","bibbaseid":"dureisseix-generalizedfractionfreelufactorizationforsingularsystemswithkernelextraction-2012","role":"author","urls":{"Paper":"http://www.sciencedirect.com/science/article/pii/S0024379511004617"},"keyword":["CFFLU","Exact factorization","Gaussian elimination","Integral domain","Linear system","mathematics","research","symbolic computation","uses sympy"],"metadata":{"authorlinks":{}},"downloads":0},"bibtype":"article","biburl":"https://bibbase.org/zotero-group/nicoguaro/525293","creationDate":"2019-12-04T16:23:11.306Z","downloads":0,"keywords":["cfflu","exact factorization","gaussian elimination","integral domain","linear system","mathematics","research","symbolic computation","uses sympy"],"search_terms":["generalized","fraction","free","factorization","singular","systems","kernel","extraction","dureisseix"],"title":"Generalized fraction-free LU factorization for singular systems with kernel extraction","year":2012,"dataSources":["YtBDXPDiQEyhyEDZC","fhHfrQgj3AaGp7e9E","qzbMjEJf5d9Lk78vE","45tA9RFoXA9XeH4MM","MeSgs2KDKZo3bEbxH","nSXCrcahhCNfzvXEY","ecatNAsyr4f2iQyGq","tpWeaaCgFjPTYCjg3"]}