{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,1,28]],"date-time":"2025-01-28T05:38:08Z","timestamp":1738042688093,"version":"3.33.0"},"reference-count":17,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[1992,12,1]],"date-time":"1992-12-01T00:00:00Z","timestamp":723168000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The International Journal of Supercomputing Applications"],"published-print":{"date-parts":[[1992,12]]},"abstract":"<jats:p> Main memory accesses for shared-memory systems or global communications (synchronizations) in message passing systems decrease the computation speed. In this paper, the standard Arnoldi algorithm for approxi mating a small number of eigenvalues, with largest (or smallest) real parts for nonsymmetric large sparse ma trices, is restructured so that only one synchronization point is required; that is, one global communication in a message passing distributed-memory machine or one global memory sweep in a shared-memory ma chine per each iteration is required. We also introduce an s-step Arnoldi method for finding a few eigenvalues of nonsymmetric large sparse matrices. This method generates reduction matrices that are similar to those generated by the standard method. One iteration of the s-step Arnoldi algorithm corresponds to s itera tions of the standard Arnoldi algorithm. The s-step method has improved data locality, minimized global communication, and superior parallel properties. These algorithms are implemented on a 64-node NCUBE\/7 Hypercube and a CRAY-2, and performance results are presented. <\/jats:p>","DOI":"10.1177\/109434209200600411","type":"journal-article","created":{"date-parts":[[2007,3,5]],"date-time":"2007-03-05T01:17:47Z","timestamp":1173057467000},"page":"407-420","source":"Crossref","is-referenced-by-count":5,"title":["An Efficient Parallel Algorithm for Extreme Eigenvalues of Sparse Nonsymmetric Matrices"],"prefix":"10.1177","volume":"6","author":[{"given":"S.K.","family":"Kim","sequence":"first","affiliation":[{"name":"DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF MINNESOTA\rMINNEAPOLIS, MINNESOTA 55455"}]},{"given":"A.T.","family":"Chronopoulos","sequence":"additional","affiliation":[{"name":"DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF MINNESOTA\rMINNEAPOLIS, MINNESOTA 55455"}]}],"member":"179","published-online":{"date-parts":[[1992,12,1]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1109\/12.9733"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(89)90045-9"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8191(89)90062-8"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8191(87)90006-8"},{"journal-title":"Conf. Parallel Computing","year":"1986","author":"Dongarra, J.J.","key":"atypb5"},{"key":"atypb6","unstructured":"Golub, G.H., and Van Loan, C.F. 1989. MATRIX Computations. Baltimore : Johns Hopkins University Press, pp. 219-225."},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1137\/0909041"},{"key":"atypb8","first-page":"17","volume":"5","author":"Kim, S.K.","year":"1991","journal-title":"Parallel Comput."},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8191(87)90012-3"},{"volume-title":"Proc. of the 1987 International Conf. on Parallel Processing","author":"Ni, L.M.","key":"atypb10"},{"key":"atypb11","unstructured":"Ranka, S., Won, Y., and Sahni, S. 1988. Programming the NCUBE Hypercube. Tech. Rep. CSci No. 88-13. Minneapolis: University of Minnesota."},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0062097"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(80)90169-X"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1984-0736453-8"},{"volume-title":"Partial eigensolutions of large nonsymmetric matrices. 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