{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,10]],"date-time":"2025-06-10T19:04:11Z","timestamp":1749582251688},"reference-count":37,"publisher":"Elsevier BV","issue":"10","license":[{"start":{"date-parts":[[1992,10,1]],"date-time":"1992-10-01T00:00:00Z","timestamp":717897600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Parallel Computing"],"published-print":{"date-parts":[[1992,10]]},"DOI":"10.1016\/0167-8191(92)90059-g","type":"journal-article","created":{"date-parts":[[2003,9,3]],"date-time":"2003-09-03T17:52:02Z","timestamp":1062611522000},"page":"1105-1128","source":"Crossref","is-referenced-by-count":19,"title":["Divide and conquer algorithms for the bandsymmetric eigenvalue problem"],"prefix":"10.1016","volume":"18","author":[{"given":"Peter","family":"Arbenz","sequence":"first","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/0167-8191(92)90059-G_BIB1","series-title":"Vector and Parallel Computing","first-page":"1","article-title":"Divide-and-conquer algorithms for the computation of the SVD of bidiagonal matrices","author":"Arbenz","year":"1989"},{"key":"10.1016\/0167-8191(92)90059-G_BIB2","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1137\/0912039","article-title":"Computing eigenvalues of banded symmetric Toeplitz matrices","volume":"12","author":"Arbenz","year":"1991","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"10.1016\/0167-8191(92)90059-G_BIB3","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/0024-3795(88)90309-6","article-title":"Restricted rank modification of the symmetric eigenvalue problem: Theoretical considerations","volume":"104","author":"Arbenz","year":"1988","journal-title":"Linear Algebra Appl."},{"key":"10.1016\/0167-8191(92)90059-G_BIB4","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1137\/0609004","article-title":"On the spectral decomposition of Hermitian matrices modified by low rank perturbations with applications","volume":"9","author":"Arbenz","year":"1988","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"10.1016\/0167-8191(92)90059-G_BIB5","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1142\/S0129053389000068","article-title":"On a block implementation of Hessenberg multishift QR iteration","volume":"1","author":"Bai","year":"1989","journal-title":"Internat. J. High Speed Comput."},{"key":"10.1016\/0167-8191(92)90059-G_BIB6","doi-asserted-by":"crossref","first-page":"828","DOI":"10.1137\/0724053","article-title":"An extension of Aronszajn's rule: Slicing the spectrum for intermediate problems","volume":"24","author":"Beattie","year":"1987","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/0167-8191(92)90059-G_BIB7","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/0024-3795(88)90178-4","article-title":"Schur complements and the Weinstein-Aronszajn theory for modified matrix eigenvalue problems","volume":"108","author":"Beattie","year":"1988","journal-title":"Linear Algebra Appl."},{"key":"10.1016\/0167-8191(92)90059-G_BIB8","series-title":"Proc. Fifth SIAM Conf. on Parallel Processing","article-title":"Parallel solution of a generalize eigenvalue problem","author":"Beattie","year":"1991"},{"key":"10.1016\/0167-8191(92)90059-G_BIB9","series-title":"Algorithms for Minimization without Derivatives","author":"Brent","year":"1973"},{"key":"10.1016\/0167-8191(92)90059-G_BIB10","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/BF01396012","article-title":"Rank-one modification of the symmetric eigenproblem","volume":"31","author":"Bunch","year":"1978","journal-title":"Numer. Math."},{"key":"10.1016\/0167-8191(92)90059-G_BIB11","series-title":"Generalized Inverses of Linear Transformation","author":"Campbell","year":"1979"},{"key":"10.1016\/0167-8191(92)90059-G_BIB12","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/BF01396757","article-title":"A divide and conquer method for the symmetric tridiagonal eigenproblem","volume":"36","author":"Cuppen","year":"1981","journal-title":"Numer. Math."},{"key":"10.1016\/0167-8191(92)90059-G_BIB13","series-title":"LINPACK User's Guide","author":"Dongarra","year":"1979"},{"key":"10.1016\/0167-8191(92)90059-G_BIB14","doi-asserted-by":"crossref","first-page":"s139","DOI":"10.1137\/0908018","article-title":"A fully parallel algorithm for the symmetric eigenvalue problem","volume":"8","author":"Dongarra","year":"1987","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"10.1016\/0167-8191(92)90059-G_BIB15","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/0167-8191(87)90016-0","article-title":"A portable environment for developing parallel FORTRAN programs","volume":"5","author":"Dongarra","year":"1987","journal-title":"Parallel Comput."},{"key":"10.1016\/0167-8191(92)90059-G_BIB16","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/0167-8191(88)90108-1","article-title":"Programming methodology and performance issues for advanced computer architectures","volume":"8","author":"Dongarra","year":"1988","journal-title":"Parallel Comput."},{"key":"10.1016\/0167-8191(92)90059-G_BIB17","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/0377-0427(89)90367-1","article-title":"Block reduction of matrices to condensed forms for eigenvalue computations","volume":"27","author":"Dongarra","year":"1989","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/0167-8191(92)90059-G_BIB18","article-title":"Matrix Eigensystem Routines \u2014 EISPACK Guide Extension","volume":"51","author":"Garbow","year":"1977"},{"key":"10.1016\/0167-8191(92)90059-G_BIB19","article-title":"Using inverse iteration to improve the divide and conquer algorithm","volume":"159","author":"Gates","year":"1991"},{"key":"10.1016\/0167-8191(92)90059-G_BIB20","article-title":"Matrix Computations","author":"Golub","year":"1989"},{"key":"10.1016\/0167-8191(92)90059-G_BIB21","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1137\/0911013","article-title":"Solving the tridiagonal eigenvalue problem on the hypercube","volume":"11","author":"Ipsen","year":"1990","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"10.1016\/0167-8191(92)90059-G_BIB22","article-title":"A case against a divide and conquer approach to the nonsymmetric eigenvalue problem","author":"Jessup","year":"1991"},{"key":"10.1016\/0167-8191(92)90059-G_BIB23","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1145\/356068.356074","article-title":"Banded eigenvalue solvers on vector machines","volume":"10","author":"Kaufman","year":"1984","journal-title":"ACM Trans. Math. Softw."},{"key":"10.1016\/0167-8191(92)90059-G_BIB24","article-title":"Parallele Reduktion symmetrischer Brandmatrizen auf Tridiagonalgestalt","author":"Lang","year":"1991"},{"key":"10.1016\/0167-8191(92)90059-G_BIB25","doi-asserted-by":"crossref","first-page":"s155","DOI":"10.1137\/0908019","article-title":"A multiprocessor algorithm for the symmetric tridiagonal eigenvalue problem","volume":"8","author":"Lo","year":"1987","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"10.1016\/0167-8191(92)90059-G_BIB26","series-title":"Parallel Processing for Scientific Computing","first-page":"82","article-title":"A parallel, hybrid algorithm for the generalized eigenproblem","author":"Ma","year":"1989"},{"key":"10.1016\/0167-8191(92)90059-G_BIB27_1","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/BF02162421","article-title":"Solution of symmetric and unsymmetric band equations and the calculation of eigenvectors of band matrices","volume":"9","author":"Martin","year":"1967","journal-title":"Numer. Math."},{"key":"10.1016\/0167-8191(92)90059-G_BIB27_2","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1007\/BF02162421","article-title":"Solution of symmetric and unsymmetric band equations and the calculation of eigenvectors of band matrices","volume":"9","author":"Martin","year":"1967","journal-title":"Numer. Math."},{"key":"10.1016\/0167-8191(92)90059-G_BIB28","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1016\/0021-9991(90)90177-3","article-title":"Computing the eigenvalues and eigenvectors of symmetric arrowhead matrices","volume":"90","author":"O'Leary","year":"1990","journal-title":"J. Comp. Phys."},{"key":"10.1016\/0167-8191(92)90059-G_BIB29","series-title":"The Symmetric Eigenvalue Problem","author":"Parlett","year":"1980"},{"key":"10.1016\/0167-8191(92)90059-G_BIB30_1","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1007\/BF02162505","article-title":"Tridiagonalization of a symmetric band matrix","volume":"12","author":"Schwarz","year":"1968","journal-title":"Numer. Math."},{"key":"10.1016\/0167-8191(92)90059-G_BIB30_2","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/BF02162505","article-title":"Tridiagonalization of a symmetric band matrix","volume":"12","author":"Schwarz","year":"1968","journal-title":"Numer. Math."},{"key":"10.1016\/0167-8191(92)90059-G_BIB31","series-title":"Large Order Structural Eigenanalysis Techniques","author":"Sehmi","year":"1989"},{"key":"10.1016\/0167-8191(92)90059-G_BIB32","article-title":"Matrix Eigensystem Routines \u2014 EISPACK Guide","volume":"6","author":"Smith","year":"1976"},{"key":"10.1016\/0167-8191(92)90059-G_BIB33","doi-asserted-by":"crossref","first-page":"1752","DOI":"10.1137\/0728087","article-title":"On the orthogonality of eigenvectors computed by divide-and-conquer techniques","volume":"28","author":"Sorensen","year":"1991","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/0167-8191(92)90059-G_BIB34","series-title":"Methods of Intermediate Problems for Eigenvalues","author":"Weinstein","year":"1972"},{"key":"10.1016\/0167-8191(92)90059-G_BIB35","series-title":"Linear Algebra","year":"1971"}],"container-title":["Parallel Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:016781919290059G?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:016781919290059G?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,2,25]],"date-time":"2019-02-25T09:27:24Z","timestamp":1551086844000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/016781919290059G"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,10]]},"references-count":37,"journal-issue":{"issue":"10","published-print":{"date-parts":[[1992,10]]}},"alternative-id":["016781919290059G"],"URL":"https:\/\/doi.org\/10.1016\/0167-8191(92)90059-g","relation":{},"ISSN":["0167-8191"],"issn-type":[{"value":"0167-8191","type":"print"}],"subject":[],"published":{"date-parts":[[1992,10]]}}}