{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T11:12:53Z","timestamp":1778584373737,"version":"3.51.4"},"reference-count":55,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2005,7,8]],"date-time":"2005-07-08T00:00:00Z","timestamp":1120780800000},"content-version":"vor","delay-in-days":3721,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numerical Linear Algebra App"],"published-print":{"date-parts":[[1995,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>With the growing demands from disciplinary and interdisciplinary fields of science and engineering for the numerical solution of the nonsymmetric eigenvalue problem, competitive new techniques have been developed for solving the problem. In this paper we examine the state of the art of the algorithmic techniques and the software scene for the problem. Some current developments are also outlined.<\/jats:p>","DOI":"10.1002\/nla.1680020304","type":"journal-article","created":{"date-parts":[[2005,11,1]],"date-time":"2005-11-01T19:21:26Z","timestamp":1130872886000},"page":"219-234","source":"Crossref","is-referenced-by-count":10,"title":["Progress in the numerical solution of the nonsymmetric eigenvalue problem"],"prefix":"10.1002","volume":"2","author":[{"given":"Zhaojun","family":"Bai","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2005,7,8]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Towards a divide and conquer algorithm for the real nonsymmetric eigenvalue problem","author":"Adams L.","year":"1991"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.2172\/5604546"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0196-8858(92)90011-K"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.2307\/2153404"},{"key":"e_1_2_1_6_2","volume-title":"Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing","author":"Bai Z.","year":"1993"},{"key":"e_1_2_1_7_2","volume-title":"SRRIT: a Fortran Subroutine to Calculate the dominant invariant subspace of a nonsymmetric matrix","author":"Bai Z.","year":"1992"},{"key":"e_1_2_1_8_2","unstructured":"N. E.Bixler.Stability of coating flow. Ph.D. thesis University of Minnesota Minneapolis MN 1982."},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/0304-8853(87)90057-6"},{"key":"e_1_2_1_10_2","unstructured":"A. G.BoudouvisandL. E.Scriven.A three\u2010dimensional patten selection scenario Technical Report 91\/248 University of Minnesota Supercomput. Inst.1991."},{"key":"e_1_2_1_11_2","unstructured":"F.ChatelinandS.Godet\u2010Thobie.Stability analysis and nonnormal matrices in aeronautical industries. In R. Vichnevetsky and J. Miller editors Proceedings of the 13th IMACS World Congress on Computation and Applied Mathematics 1991."},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01065178"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-0208(08)72647-1"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/0010-4655(89)90147-1"},{"key":"e_1_2_1_15_2","unstructured":"D.Day.Semi\u2010duality in the two\u2010sided Lanczos algorithm. Ph.D. thesis University of California at Berkeley 1993."},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971811"},{"key":"e_1_2_1_17_2","doi-asserted-by":"publisher","DOI":"10.1137\/0914035"},{"key":"e_1_2_1_18_2","unstructured":"A.Dubrulle.The multishift QR algorithm: is it worth the trouble?Palo Alto Scientific Center Reprort G320\u20103558x IBM Corp. 1991."},{"key":"e_1_2_1_19_2","doi-asserted-by":"publisher","DOI":"10.1145\/152613.152614"},{"key":"e_1_2_1_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(85)90054-3"},{"key":"e_1_2_1_21_2","unstructured":"R.FreundandN.Nachtigal.An Implementation of the Look\u2010Ahead Lanczos Algorithm for Non\u2010Hermitian Matrices Part II. Technical Report TR 90\u201346 RIACS Nov.1990."},{"key":"e_1_2_1_22_2","unstructured":"A.Galick T.KerkhovenandU.Ravaioli.Iterative solution of the eigenvalue problem for a dielectric wageguide. CSRD Reprot 1119 University of Illinois at Urbana\u2010Champaign July1991."},{"key":"e_1_2_1_23_2","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-08254-9"},{"key":"e_1_2_1_24_2","volume-title":"Bifurcation and Chaos: Analysis, Algorithms, Applications","author":"Garratt T. J.","year":"1991"},{"key":"e_1_2_1_25_2","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1137\/0613024","article-title":"Sparse matrices in MATLAB: design and implementation","volume":"13","author":"Gilbert J.","year":"1992","journal-title":"SIAM J. Mat. Anal. Appl."},{"key":"e_1_2_1_26_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01061511"},{"key":"e_1_2_1_27_2","volume-title":"Matrix Computations","author":"Golub G.","year":"1989"},{"key":"e_1_2_1_28_2","series-title":"Technical Report CTC\u2010TR\u2010100","volume-title":"Increasing data reuse in the unsymmetric QR algorithm","author":"Henry G.","year":"1992"},{"key":"e_1_2_1_29_2","doi-asserted-by":"publisher","DOI":"10.1145\/50063.214386"},{"key":"e_1_2_1_30_2","doi-asserted-by":"crossref","unstructured":"E.Jessup.A case against a divide and conquer approach to the nonsymmetric eigenproblem. Technical Report ONRL\/TM\u201011903 Oak Ridge National Laboratory 1991.","DOI":"10.2172\/5926172"},{"key":"e_1_2_1_31_2","doi-asserted-by":"publisher","DOI":"10.1137\/0719030"},{"key":"e_1_2_1_32_2","doi-asserted-by":"publisher","DOI":"10.2307\/2153068"},{"key":"e_1_2_1_33_2","volume-title":"Dept. of Comp. Sci. TRCS 91\u201015","author":"Lin C\u2010C.","year":"1991"},{"key":"e_1_2_1_34_2","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(91)90006-7"},{"key":"e_1_2_1_35_2","doi-asserted-by":"crossref","unstructured":"N.Martins. Efficient eigenvalue and frequency response methods applied to power system small\u2010signal stability studies.IEEE Trans. on Power Systems PWRS\u20101 217\u2013226 1986.","DOI":"10.1109\/TPWRS.1986.4334874"},{"key":"e_1_2_1_36_2","doi-asserted-by":"publisher","DOI":"10.1137\/0905042"},{"key":"e_1_2_1_37_2","doi-asserted-by":"crossref","DOI":"10.21236\/ADA256581","volume-title":"The method of minimal representation in 2D Ising model calculations","author":"Parlett B.","year":"1992"},{"key":"e_1_2_1_38_2","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(87)90126-1"},{"key":"e_1_2_1_39_2","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(84)90221-0"},{"key":"e_1_2_1_40_2","first-page":"149","volume-title":"Recent Advances in Iterative Methods, IMA Volumes in Mathematics and its Applications 60","author":"Ruhe A.","year":"1993"},{"key":"e_1_2_1_41_2","doi-asserted-by":"publisher","DOI":"10.1137\/0906059"},{"key":"e_1_2_1_42_2","doi-asserted-by":"publisher","DOI":"10.1137\/0724013"},{"key":"e_1_2_1_43_2","doi-asserted-by":"publisher","DOI":"10.1016\/0010-4655(89)90149-5"},{"key":"e_1_2_1_44_2","unstructured":"Y.Saad.SPARSKIT: A basic tool kit for sparse matrix computation. CSRD Report 1029 University of Illinois at Urbana\u2010Champaign August 1990."},{"key":"e_1_2_1_45_2","volume-title":"Numerical Methods for Large Eigenvalue Problems","author":"Saad Y.","year":"1992"},{"key":"e_1_2_1_46_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01388687"},{"key":"e_1_2_1_47_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01388686"},{"key":"e_1_2_1_48_2","first-page":"123","article-title":"Two\u2010dimensional analysis of optical waveguides with a nonuniform finite difference method","volume":"138","author":"Seki S.","year":"1991","journal-title":"IEE Procedings\u2010J"},{"key":"e_1_2_1_49_2","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-07546-1"},{"key":"e_1_2_1_50_2","doi-asserted-by":"publisher","DOI":"10.1137\/0613025"},{"key":"e_1_2_1_51_2","unstructured":"D.SorensenandP.Vu. Private communication 1992."},{"key":"e_1_2_1_52_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01462265"},{"key":"e_1_2_1_53_2","series-title":"Dept. of Comp. Sci. TR 154","volume-title":"SRRIT: a Fortran subroutine to calculate the dominant invariant subspace of a nonsymmetric matrix","author":"Stewart G. W.","year":"1978"},{"key":"e_1_2_1_54_2","doi-asserted-by":"publisher","DOI":"10.1145\/355945.355952"},{"key":"e_1_2_1_55_2","unstructured":"P.Van Dooren.Block shifts and block QR. Presentation at SIAM Conf. on Appl. Lin. Alg. Minneapolis MN September 1991. SIAM. Philadelphia PA 1991."},{"key":"e_1_2_1_56_2","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(91)90004-G"}],"container-title":["Numerical Linear Algebra with Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnla.1680020304","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/nla.1680020304","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,11]],"date-time":"2023-09-11T02:39:57Z","timestamp":1694399997000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/nla.1680020304"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,5]]},"references-count":55,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1995,5]]}},"alternative-id":["10.1002\/nla.1680020304"],"URL":"https:\/\/doi.org\/10.1002\/nla.1680020304","archive":["Portico"],"relation":{},"ISSN":["1070-5325","1099-1506"],"issn-type":[{"value":"1070-5325","type":"print"},{"value":"1099-1506","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,5]]}}}