{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T06:41:01Z","timestamp":1697956861028},"reference-count":17,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2007,3,21]],"date-time":"2007-03-21T00:00:00Z","timestamp":1174435200000},"content-version":"vor","delay-in-days":7384,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems &amp; Computers in Japan"],"published-print":{"date-parts":[[1987,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The analysis of a nonlinear network is reduced to the solution of a system of equations at each step of Newton's method. In the solution by the direct method, the highspeed realization of the LU decomposition of an large\u2010scale sparse matrix has become important with the development of the integrated technology. In the past, the applications of the array processor and the supercomputer have been considered. However, the array processor cannot utilize the sparsity of the matrix, resulting in an impractical system with too many processor cells. The efficiency of the vectorization is a problem in the super\u2010computer, when it is used for the Gauss elimination only for the nonzero elements in the matrix. This paper proposes a dedicated processor for LU decomposition of a large\u2010scale sparse matrix, which can utilize the sparsity of the matrix and can be realized with a practical number of processors. The processor is composed of <jats:italic>q<\/jats:italic> local units, corresponding to the nonzero elements in each row of the coefficient matrix, and those units operate in parallel. In the processing of a sparse matrix, the matching of the label is required in the Gauss elimination. It is realized with a high speed by the data\u2010shift operation by the inter\u2010register transfer. Furthermore, a processor with a hierarchical memory structure is proposed which can cope with the case where the number <jats:italic>p<\/jats:italic> of nonzero elements in a row exceeds <jats:italic>q<\/jats:italic>.<\/jats:p>","DOI":"10.1002\/scj.4690180608","type":"journal-article","created":{"date-parts":[[2007,7,7]],"date-time":"2007-07-07T13:52:26Z","timestamp":1183816346000},"page":"89-99","source":"Crossref","is-referenced-by-count":1,"title":["Special parallel processor for lu decomposition of a large\u2010scale sparse matrix"],"prefix":"10.1002","volume":"18","author":[{"given":"Hideki","family":"Asai","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mitsuo","family":"Asai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mamoru","family":"Tanaka","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2007,3,21]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"65","volume-title":"Advances in Computers","author":"Kung H. T.","year":"1980"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-68402-9"},{"key":"e_1_2_1_4_2","first-page":"296","volume-title":"A Systolic Data Structure Chip for Connectivity Problems","author":"Savage C.","year":"1981"},{"issue":"2","key":"e_1_2_1_5_2","first-page":"175","article-title":"BC processor array and highly parallel matrix computation","volume":"24","author":"Kanada Y.","year":"1983","journal-title":"Trans. Inf. Proc. Soc. Jap."},{"issue":"12","key":"e_1_2_1_6_2","first-page":"1416","article-title":"A bit\u2010serial parallel processor for LU decomposition","volume":"66","author":"Shimizu N.","year":"1983","journal-title":"Trans. (D), I. E. C. E., Japan"},{"key":"e_1_2_1_7_2","volume-title":"Numerical Computation","author":"Fukao T.","year":"1982"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCT.1971.1083215"},{"issue":"12","key":"e_1_2_1_9_2","first-page":"1467","article-title":"Computer for symbolic analysis of active circuits by two\u2010graph method\u2010Tree generator","volume":"65","author":"Tanaka M.","year":"1982","journal-title":"Trans. (D), I. E. C. E., Japan"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1109\/TC.1983.1676171"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1981.1084988"},{"key":"e_1_2_1_12_2","article-title":"A Special Parallel Processor for LU Decomposition of a Large\u2010Scale Sparse Matrix","volume":"1985","author":"Asai H.","year":"1985","journal-title":"I. E. E. E. Proc. Int. Symp. Circuits and Systems"},{"key":"e_1_2_1_13_2","article-title":"A construction of LU decomposition\u2010dedicated computer for large\u2010scale sparse matrices","volume":"84","author":"Asai H.","year":"1985","journal-title":"Tech. Rep. I. E. C. E., Japan"},{"key":"e_1_2_1_14_2","volume-title":"Super\u2010computers competing in speed","author":"Tanaka Z.","year":"1983"},{"key":"e_1_2_1_15_2","first-page":"2","volume-title":"Super\u2010computer, Computer Today, July","author":"Karaki Y.","year":"1984"},{"issue":"12","key":"e_1_2_1_16_2","first-page":"1290","article-title":"Super\u2010computer and computational physics","volume":"67","author":"Kawai T.","year":"1984","journal-title":"Proc. I. E. C. E., Japan"},{"issue":"12","key":"e_1_2_1_17_2","first-page":"853","article-title":"Processor array PAX\u2010128","volume":"67","author":"Shirakawa T.","year":"1984","journal-title":"Trans. (D), I. E. C. E., Japan"},{"key":"e_1_2_1_18_2","doi-asserted-by":"publisher","DOI":"10.1109\/PROC.1977.10514"}],"container-title":["Systems and Computers in Japan"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fscj.4690180608","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/scj.4690180608","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T02:30:28Z","timestamp":1697855428000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/scj.4690180608"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1987,1]]},"references-count":17,"journal-issue":{"issue":"6","published-print":{"date-parts":[[1987,1]]}},"alternative-id":["10.1002\/scj.4690180608"],"URL":"https:\/\/doi.org\/10.1002\/scj.4690180608","archive":["Portico"],"relation":{},"ISSN":["0882-1666","1520-684X"],"issn-type":[{"value":"0882-1666","type":"print"},{"value":"1520-684X","type":"electronic"}],"subject":[],"published":{"date-parts":[[1987,1]]}}}