{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:27:48Z","timestamp":1787336868641,"version":"build-2736575974"},"reference-count":41,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2000,1]]},"abstract":"<jats:p>Standard preconditioners, like incomplete factorizations, perform well when the coefficient matrix is diagonally dominant, but often fail on general sparse matrices. We experiment with nonsymmetric permutations and scalings aimed at placing large entries on the diagonal in the context of preconditioning for general sparse matrices. The permutations and scalings are those developed by Olschowka and Neumaier [Linear Algebra Appl., 240 (1996), pp. 131--151] and by Duff and Koster [SIAM J. Matrix Anal. Appl., 20 (1999), pp. 889--901; Tech. report Ral-Tr-99-030, Rutherford Appleton Laboratory, Chilton, UK, 1999]. We target highly indefinite, nonsymmetric problems that cause difficulties for preconditioned iterative solvers. Our numerical experiments indicate that the reliability and performance of preconditioned iterative solvers are greatly enhanced by such preprocessing.<\/jats:p>","DOI":"10.1137\/s1064827599361308","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1333-1353","source":"Crossref","is-referenced-by-count":102,"title":["Preconditioning Highly Indefinite and Nonsymmetric Matrices"],"prefix":"10.1137","volume":"22","author":[{"given":"Michele","family":"Benzi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"John C.","family":"Haws","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Miroslav","family":"Tuma","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,2,17]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1177\/109434209901300202"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827599356900"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827594271421"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827597326845"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827595294691"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-9274(98)00118-4"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827598339372"},{"key":"R8","unstructured":"W. Bomhof and H. A. van der Vorst,\n                      A parallel linear system solver for circuit simulation problems\n                      , Numer. Linear Algebra Appl., submitted."},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827598335842"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(97)00171-4"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1016\/0098-1354(95)00074-7"},{"key":"R12","unstructured":"T. Davis,\n                      University of Florida Sparse Matrix Collection\n                      , University of Florida, Gainesville, FL, available online from http:\/\/www.cise.ufl.edu\/\u02dcdavis\/sparse\/."},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1007\/BF01386390"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1145\/355958.355963"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1145\/355958.355968"},{"key":"R16","volume-title":"Direct methods for sparse matrices","author":"Duff I.","year":"1989"},{"key":"R17","unstructured":"I. S. Duff, R. G. Grimes, and J. G. Lewis,\n                      The Rutherford\u2013Boeing Sparse Matrix Collection\n                      , Technical Report RAL\u2010TR\u201097\u2010031, Rutherford Appleton Laboratory, Chilton, UK, 1997."},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479897317661"},{"key":"R19","unstructured":"I. S. Duff and J. Koster,\n                      On Algorithms for Permuting Large Entries to the Diagonal of a Sparse Matrix\n                      , Technical Report RAL\u2010TR\u201099\u2010030, Rutherford Appleton Laboratory, Chilton, UK, 1999."},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1007\/BF01932738"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.6028\/jres.069B.013"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1986-0842130-7"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1137\/0914029"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-1889(98)00012-8"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1007\/BF03008919"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827594276552"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827595288425"},{"key":"R28","unstructured":"S. A. Kharchenko, L. Yu. Kolotilina, A. A. Nikishin, and A. Yu. Yeremin,\n                      A Robust AINV\u2010Type Preconditioning Method for Constructing Sparse Approximate Inverse Preconditioners in Factored Form\n                      , preprint, Russian Academy of Sciences, Moscow, 1999."},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1137\/0614004"},{"key":"R30","unstructured":"X. S. Li and J. W. Demmel,\n                      Making sparse Gaussian elimination scalable by static pivoting\n                      , in Proceedings of the SuperComputing\u201898 Conference, CD\u2010ROM, ACM, New York, 1998."},{"key":"R31","doi-asserted-by":"publisher","DOI":"10.1137\/0716027"},{"key":"R32","doi-asserted-by":"publisher","DOI":"10.1145\/214392.214398"},{"key":"R33","doi-asserted-by":"publisher","DOI":"10.1016\/0898-1221(94)90064-7"},{"key":"R34","first-page":"148","volume":"31","author":"Meijerink J. A.","year":"1977","journal-title":"Math. Comp."},{"key":"R35","unstructured":"Matrix Market\n                      , National Institute of Standards and Technology, Gaithersburg, MD, available online from http:\/\/math.nist.gov\/MatrixMarket."},{"key":"R36","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(94)00192-8"},{"key":"R37","unstructured":"G. Pauletto,\n                      Solution and Simulation of Macroeconometric Models\n                      , Ph.D. thesis, Department of Econometrics, University of Geneva, Switzerland, 1995."},{"key":"R38","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(88)90345-7"},{"key":"R39","unstructured":"J. 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