{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:35:21Z","timestamp":1787333721481,"version":"build-2736575974"},"reference-count":29,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[1997,9]]},"abstract":"<jats:p>We describe a parallelizable Jacobi-type block Broyden algorithm for solving nonlinear systems of equations. We study the conditions under which the algorithm is locally convergent. Basically, the Jacobian matrix in a Newton algorithm is replaced by a block Broyden-like matrix which can be easily calculated by a recurrence relation. A family of nonlinear solvers could be generated combining it with some iterative or direct linear solvers. Different initializations for the block Broyden matrix are proposed, as well as several partitioning schemes, producing an effective block partitioning of the Jacobian matrix. Coupled with the restarted version of the linear GMRES(m) algorithm, the method parallelizes very well and gives good CPU time savings, which are shown by several numerical tests.<\/jats:p>","DOI":"10.1137\/s1064827595285172","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1367-1392","source":"Crossref","is-referenced-by-count":10,"title":["Inexact Block Jacobi--Broyden Methods for Solving Nonlinear Systems of Equations"],"prefix":"10.1137","volume":"18","author":[{"given":"Geng","family":"Yang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Laura C.","family":"Dutto","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michel","family":"Fortin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"J. All\u00e9gre, M. Raffin, and J. C. Lengrand,\n                      Experimental flow fields around NACA 0012 airfoils located in subsonic and supersonic rarefied air streams\n                      , in Numerical Simulation of Compressible Navier\u2010Stokes Flows, M.\u2010O. Bristeau, R. Glowinski, J. P\u00e9riaux, and H. Viviand, eds., Notes on Numerical Fluid Mechanics 18, Friedr. Viewag & Sohn, Braunschweig\/Wiesbaden, Germany, 1987, pp. 59\u201368.","DOI":"10.1007\/978-3-322-87873-1_3"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/0915020"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"S. T. Barnard and H. D. Simon,\n                      A fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems\n                      , in Proc. 6th SIAM Conf. 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Schnabel,\n                      Numerical Methods for Unconstrained Optimization and Nonlinear Equations\n                      , Prentice\u2013Hall, Englewood Cliffs, NJ, 1983."},{"key":"R11","unstructured":"R. Dias da Cunha and T. R. Hopkins,\n                      PIM 1:1: The Parallel Iterative Methods Package for Systems of Linear Equations, User\u2019s Guide (Fortran 77 Version)\n                      , Computing Laboratory, University of Kent at Canterbury, UK, February 1994."},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1620360307"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(94)90075-2"},{"key":"R14","doi-asserted-by":"crossref","unstructured":"R. Fletcher,\n                      Conjugate gradient methods for indefinite systems\n                      , in Numerical Analysis Dundee, G. A. 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Leland,\n                      The Chaco User\u2019s Guide, Version 1:0\n                      , Tech. report SAND, 93\u20102339, Sandia National Laboratories, Albuquerque, NM, 1993.","DOI":"10.2172\/10106339"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1970.tb01770.x"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1137\/0729081"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1137\/0731011"},{"key":"R23","doi-asserted-by":"crossref","unstructured":"J. M. Mart\u00ednez,\n                      Algorithms for solving nonlinear systems of equations\n                      , in Algorithms for Continuous Optimization: The State of the Art, M. Spedicato, ed., NATO ASI Series, Kluwer, Norwell, MA, 1994, pp. 81\u2013108.","DOI":"10.1007\/978-94-009-0369-2_4"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1137\/0911048"},{"key":"R25","unstructured":"J. M. Ortega and W. C. 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