{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T15:15:32Z","timestamp":1760886932516,"version":"3.43.0"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2000,5,1]],"date-time":"2000-05-01T00:00:00Z","timestamp":957139200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2000,5,1]],"date-time":"2000-05-01T00:00:00Z","timestamp":957139200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Reliable Computing"],"published-print":{"date-parts":[[2000,5]]},"DOI":"10.1023\/a:1009961021112","type":"journal-article","created":{"date-parts":[[2002,12,22]],"date-time":"2002-12-22T19:25:11Z","timestamp":1040585111000},"page":"123-137","source":"Crossref","is-referenced-by-count":2,"title":["Jacobi and Gauss-Seidel Iterations for Polytopic Systems: Convergence via Convex M-Matrices"],"prefix":"10.1007","volume":"6","author":[{"given":"Du\u0161an M.","family":"Stipanovi\u0107","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dragoslav D.","family":"\u0160iljak","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"261617_CR1","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1137\/1037008","volume":"37","author":"R. Bagnara","year":"1995","unstructured":"Bagnara, R.: A Unified Proof for the Convergence of Jacobi and Gauss-Seidel Methods, SIAM Review\n37 (1995), pp. 93-97.","journal-title":"SIAM Review"},{"key":"261617_CR2","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1109\/71.508248","volume":"7","author":"B. Bar\u00e1n","year":"1996","unstructured":"Bar\u00e1n, B., Kaszkurewicz, E. and Bhaya, A.: Parallel Asynchronous Team Algorithms: Convergence and Performance Analysis, IEEE Transactions on Parallel and Distributed Systems\n7 (1996), pp. 677-688.","journal-title":"IEEE Transactions on Parallel and Distributed Systems"},{"key":"261617_CR3","volume-title":"Nonnegative Matrices in the Mathematical Sciences","author":"A. Berman","year":"1979","unstructured":"Berman, A. and Plemmons, R.J.: Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, 1979."},{"key":"261617_CR4","volume-title":"Parallel and Distributed Computation: Numerical Methods","author":"D.P. Bertsekas","year":"1989","unstructured":"Bertsekas, D.P. and Tsitsiklis, J.N.: Parallel and Distributed Computation: Numerical Methods, Prentice-Hall, Englewood Cliffs, NJ, 1989."},{"key":"261617_CR5","doi-asserted-by":"crossref","first-page":"762","DOI":"10.1109\/9.489221","volume":"41","author":"A. Bhaya","year":"1996","unstructured":"Bhaya, A. and Kaszkurewicz, E.: Comments Regarding \u201cOn Stability of Interval Matrices,\u201d IEEE Transactions on Automatic Control\n41 (1996), pp. 762-766.","journal-title":"IEEE Transactions on Automatic Control"},{"key":"261617_CR6","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970777","volume-title":"Linear Matrix Inequalities in System and Control Theory","author":"S. Boyd","year":"1994","unstructured":"Boyd, S., Ghaoui, L. E., Feron, E., and Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, PA, 1994."},{"key":"261617_CR7","first-page":"105","volume-title":"Inequalities","author":"K. Fan","year":"1967","unstructured":"Fan, K.: Inequalities for the Sum of Two M-Matrices, in: Shisha, O. (ed.), Inequalities, Academic Press, New York, 1967, pp. 105-117."},{"key":"261617_CR8","doi-asserted-by":"crossref","first-page":"382","DOI":"10.21136\/CMJ.1962.100526","volume":"12","author":"M. Fiedler","year":"1962","unstructured":"Fiedler, M. and Pt\u00e1k, V.: On Matrices with Non-Positive Off-Diagonal Elements and Positive Minors, Czechoslovakian Mathematical Journal\n12 (1962), pp. 382-400.","journal-title":"Czechoslovakian Mathematical Journal"},{"key":"261617_CR9","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/BF01360282","volume":"159","author":"D. Gale","year":"1965","unstructured":"Gale, D. and Nikaido, H.: The Jacobian Matrix and Global Univalence of Mappings, Mathematische Annalen\n159 (1965), pp. 81-93.","journal-title":"Mathematische Annalen"},{"key":"261617_CR10","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1137\/0611006","volume":"11","author":"J. Garloff","year":"1990","unstructured":"Garloff, J.: Block Methods for the Solution of Linear Interval Equations, SIAM Journal of Matrix Analysis and Applications\n11 (1990), pp. 89-106.","journal-title":"SIAM Journal of Matrix Analysis and Applications"},{"key":"261617_CR11","volume-title":"Global Optimization Using Interval Analysis","author":"E. Hansen","year":"1992","unstructured":"Hansen, E.: Global Optimization Using Interval Analysis, Marcel Dekker, New York, 1992."},{"key":"261617_CR12","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1109\/TAC.1976.1101350","volume":"AC-21","author":"H.P. Horisberger","year":"1976","unstructured":"Horisberger, H.P. and Belanger, P.R.: Regulators for Linear, Time Invariant Plants with Uncertain Parameters, IEEE Transactions on Automatic Control\nAC-21 (1976), pp. 705-708.","journal-title":"IEEE Transactions on Automatic Control"},{"key":"261617_CR13","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511840371","volume-title":"Topics in Matrix Analysis","author":"R. A. Horn","year":"1991","unstructured":"Horn, R. A. and Johnson, C. R.: Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991."},{"key":"261617_CR14","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1137\/0709035","volume":"9","author":"J. J. Mor\u00e9","year":"1972","unstructured":"Mor\u00e9, J. J.: Nonlinear Generalizations of Matrix Diagonal Dominance with Application to Gauss-Seidel Iterations, SIAM Journal on Numerical Analysis\n9 (1972), pp. 357-378.","journal-title":"SIAM Journal on Numerical Analysis"},{"key":"261617_CR15","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/0024-3795(73)90006-2","volume":"6","author":"J. J. Mor\u00e9","year":"1973","unstructured":"Mor\u00e9, J. J. and Rheinboldt, W.: On P-and S-Functions and Related Classes of n-dimensional Nonlinear Mappings, Linear Algebra and Its Applications\n6 (1973), pp. 45-68.","journal-title":"Linear Algebra and Its Applications"},{"key":"261617_CR16","volume-title":"Studies in Applied Mathematics","author":"Y. Nesterov","year":"1994","unstructured":"Nesterov, Yu. and Nemirovsky, A.: An Interior-Point Polynomial Methods in Convex Programming, Studies in Applied Mathematics, volume 13, SIAM, Philadelphia, PA, 1994."},{"key":"261617_CR17","volume-title":"Interval Methods for Systems of Equations","author":"A. Neumaier","year":"1990","unstructured":"Neumaier, A.: Interval Methods for Systems of Equations, Cambridge University Press, Cambridge, 1990."},{"key":"261617_CR18","volume-title":"Convex Structures and Economic Theory","author":"H. Nikaido","year":"1968","unstructured":"Nikaido, H.: Convex Structures and Economic Theory, Academic Press, New York, 1968."},{"key":"261617_CR19","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1016\/0022-247X(85)90250-1","volume":"112","author":"Y. Ohta","year":"1985","unstructured":"Ohta, Y. and \u0160iljak, D. D.: Overlapping Block Diagonal Dominance and Existence of Liapunov Functions, Journal of Mathematical Analysis and Applications\n112 (1985), pp. 396-410.","journal-title":"Journal of Mathematical Analysis and Applications"},{"key":"261617_CR20","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1016\/0022-247X(70)90298-2","volume":"32","author":"W. C. Rheinboldt","year":"1970","unstructured":"Rheinboldt, W. C.: On M-functions and Their Applications to Nonlinear Gauss-Seidel Iterations and Network Flows, Journal of Mathematical Analysis and Applications\n32 (1970), pp. 275-307.","journal-title":"Journal of Mathematical Analysis and Applications"},{"key":"261617_CR21","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1109\/9.272336","volume":"39","author":"M. E. Sezer","year":"1994","unstructured":"Sezer, M. E. and \u0160iljak, D. D.: On Stability of Interval Matrices, IEEE Transactions on Automatic Control\n39 (1994), pp. 368-371.","journal-title":"IEEE Transactions on Automatic Control"},{"key":"261617_CR22","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1080\/10236199508808014","volume":"1","author":"D. D. \u0160iljak","year":"1995","unstructured":"\u0160iljak, D. D. and Ze\u010devi\u0107, A. I.: Overlapping Block-Iterative Methods for Solving Algebraic Equations, Journal of Difference Equations and Applications\n1 (1995), pp. 125-136.","journal-title":"Journal of Difference Equations and Applications"},{"key":"261617_CR23","doi-asserted-by":"crossref","unstructured":"Stipanovi\u0107, D. M. and \u0160iljak, D. D.: Convex M-Matrices and Polytopic Dynamic Systems, in: Proceedings of the 36th Conference on Decision and Control, San Diego, CA, 1997, pp. 4366-4368.","DOI":"10.1109\/CDC.1997.649590"},{"key":"261617_CR24","volume-title":"Matrix Iterative Analysis","author":"R. S. Varga","year":"1962","unstructured":"Varga, R. S.: Matrix Iterative Analysis, Prentice Hall, Englewood Cliffs, NJ, 1962."},{"key":"261617_CR25","doi-asserted-by":"crossref","first-page":"824","DOI":"10.1137\/S0895479892229115","volume":"15","author":"A. I. Ze\u010devi\u0107","year":"1994","unstructured":"Ze\u010devi\u0107, A. I. and \u0160iljak, D. D.: A Block-Parallel Newton Method via Overlapping Epsilon Decomposition, SIAM Journal of Matrix Analysis and Applications\n15 (1994), pp. 824-844.","journal-title":"SIAM Journal of Matrix Analysis and Applications"}],"container-title":["Reliable Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1009961021112.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1009961021112\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1009961021112.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T09:42:28Z","timestamp":1754473348000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1009961021112"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,5]]},"references-count":25,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2000,5]]}},"alternative-id":["261617"],"URL":"https:\/\/doi.org\/10.1023\/a:1009961021112","relation":{},"ISSN":["1385-3139","1573-1340"],"issn-type":[{"type":"print","value":"1385-3139"},{"type":"electronic","value":"1573-1340"}],"subject":[],"published":{"date-parts":[[2000,5]]}}}