{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,24]],"date-time":"2023-10-24T05:40:15Z","timestamp":1698126015800},"reference-count":15,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,24]],"date-time":"2006-10-24T00:00:00Z","timestamp":1161648000000},"content-version":"vor","delay-in-days":5624,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Concurrency: Pract. Exper."],"published-print":{"date-parts":[[1991,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The solution of the algebraic eigenvalue problem is an important component of many applications in science and engineering. With the advent of novel architecture machines, much research effort is now being expended in the search for parallel algorithms for the computation of eigensystems which can gainfully exploit the processing power which these machines provide. Among important recent work References 1\u20104 address the real symmetric eigenproblem in both its dense and sparse forms, Reference 5 treats the unsymmetric eigenproblem, and Reference 6 investigates the solution of the generalized eigenproblem. In this paper two algorithms for the parallel computation of the eigensolution of Hermitian matrices on an array processor are presented. These algorithms are based on the Parallel Orthogonal Transformation algorithm (POT) for the solution of real symmetric matrices[7,8]. POT was developed to exploit the SIMD parallelism supported by array processors such as the AMT DAP 510. The new algorithms use the highly efficient implementation strategies devised for use in POT. The implementations of the algorithms permit the computation of the eigensolution of matrices whose order exceeds the mesh size of the array processor used. A comparison of the efficiency of the two algorithms for the solution of a variety of matrices is given.<\/jats:p>","DOI":"10.1002\/cpe.4330030304","type":"journal-article","created":{"date-parts":[[2006,11,17]],"date-time":"2006-11-17T16:17:13Z","timestamp":1163780233000},"page":"179-185","source":"Crossref","is-referenced-by-count":4,"title":["The parallel computation of eigenvalues and eigenvectors of large Hermitian matrices using the AMT DAP 510"],"prefix":"10.1002","volume":"3","author":[{"given":"J. S.","family":"Weston","sequence":"first","affiliation":[]},{"given":"M.","family":"Clint","sequence":"additional","affiliation":[]},{"given":"C. W.","family":"Bleakney","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,24]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1137\/0908018"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1137\/0908019"},{"key":"e_1_2_1_4_2","unstructured":"Ipsen I.andE.Jessop Two methods for solving the symmetric tridiagonal eigenvalue problem on the hypercube inHypercube Multiprocessors1987 627\u2013638 SIAM 1987."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01389496"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8191(90)90147-2"},{"key":"e_1_2_1_7_2","first-page":"82","volume-title":"Parallel Processing for Scientific Computing","author":"Ma S.","year":"1989"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1080\/00207168408803415"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1093\/comjnl\/28.3.340"},{"key":"e_1_2_1_10_2","volume-title":"The Algebraic Eigenvalue Problem","author":"Wilkinson J. H.","year":"1965"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8191(90)90130-2"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-53065-7_152"},{"key":"e_1_2_1_13_2","unstructured":"Clint M. Weston J. S.andC. W.Bleakney \u2018A tree\u2010structured parallel algorithm for the eigensolution of large sparse symmetric matrices on an array processor\u2019 Abstracts Parallel Computing: Achievements Problems and Prospects(1990) 77\u201378 Capri 1990."},{"key":"e_1_2_1_14_2","unstructured":"Numerical Algorithms Group NAG Fortran Library 13 Oxford and Illinois 1988."},{"key":"e_1_2_1_15_2","volume-title":"Introduction to Matrix Computations","author":"Stewart G. W.","year":"1973"},{"key":"e_1_2_1_16_2","first-page":"165","volume-title":"Parallel Computing 89","author":"Weston J. S.","year":"1990"}],"container-title":["Concurrency: Practice and Experience"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fcpe.4330030304","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/cpe.4330030304","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T03:33:46Z","timestamp":1698032026000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/cpe.4330030304"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,6]]},"references-count":15,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1991,6]]}},"alternative-id":["10.1002\/cpe.4330030304"],"URL":"https:\/\/doi.org\/10.1002\/cpe.4330030304","archive":["Portico"],"relation":{},"ISSN":["1040-3108","1096-9128"],"issn-type":[{"value":"1040-3108","type":"print"},{"value":"1096-9128","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,6]]}}}