{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T23:38:30Z","timestamp":1773358710513,"version":"3.50.1"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2006,4,1]],"date-time":"2006-04-01T00:00:00Z","timestamp":1143849600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Reliable Comput"],"published-print":{"date-parts":[[2006,4]]},"DOI":"10.1007\/s11155-006-4875-1","type":"journal-article","created":{"date-parts":[[2005,12,7]],"date-time":"2005-12-07T19:44:53Z","timestamp":1133984693000},"page":"121-140","source":"Crossref","is-referenced-by-count":25,"title":["Outer Interval Solution of the Eigenvalue Problem under General Form Parametric Dependencies"],"prefix":"10.1007","volume":"12","author":[{"given":"Lubomir V.","family":"Kolev","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"4875_CR1","volume-title":"Introduction to Interval Computations","author":"G. Alefeld","year":"1983","unstructured":"Alefeld, G. and Herzberger, J.: Introduction to Interval Computations, Academic Press, New York, 1983."},{"key":"4875_CR2","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/BF02242019","volume":"47","author":"H. Behnke","year":"1991","unstructured":"Behnke, H.: The Calculation of Guaranteed Bounds for Eigenvalues Using Complementary Variational Principles, Computing 47 (1991), pp. 11\u201327.","journal-title":"Computing"},{"key":"4875_CR3","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1109\/9.272338","volume":"39","author":"J. C. Commercon","year":"1994","unstructured":"Commercon, J. C.: Eigenvalues of Tridiagonal Symmetric Interval Matrices, IEEE Transactions on Automatic Control 39 (1994), pp. 377\u2013379.","journal-title":"IEEE Transactions on Automatic Control"},{"key":"4875_CR4","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1002\/zamm.19910710117","volume":"71","author":"A. S. Deif","year":"1991","unstructured":"Deif, A. S.: The Interval Eigenvalue Problem, Zeitschrifi f\u00fcr Angewandte Mathematik und Mechanik 71 (1991), pp. 61\u201364.","journal-title":"Zeitschrifi f\u00fcr Angewandte Mathematik und Mechanik"},{"key":"4875_CR5","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1109\/81.215345","volume":"40","author":"D. Hertz","year":"1993","unstructured":"Hertz, D.: The Maximal Eigenvalue and Stability of a Class of Real Symmetric Interval Matrices, IEEE Transactions on Circuits and Systems 40 (1993), pp. 56\u201357.","journal-title":"IEEE Transactions on Circuits and Systems"},{"issue":"1","key":"4875_CR6","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/BF02390521","volume":"1","author":"C. Jager","year":"1995","unstructured":"Jager, C. and Ratz, D.: A Combined Method for Enclosing All Solutions of Nonlinear Systems of Polynomial Equations. Reliable Computing 1 (1) (1995), pp. 41\u201364.","journal-title":"Reliable Computing"},{"issue":"1","key":"4875_CR7","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1023\/A:1011470916953","volume":"7","author":"L. Kolev","year":"2001","unstructured":"Kolev, L.: Automatic Computation of a Linear Interval Enclosure, Reliable Computing 7 (1) (2001), pp. 17\u201328.","journal-title":"Reliable Computing"},{"key":"4875_CR8","doi-asserted-by":"crossref","DOI":"10.1142\/2039","volume-title":"Interval Methods for Circuit Analysis","author":"L. Kolev","year":"1993","unstructured":"Kolev, L.: Interval Methods for Circuit Analysis, World Scientific Ltd., Singapore, 1993."},{"issue":"1","key":"4875_CR9","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1023\/A:1009902813842","volume":"3","author":"L. Kolev","year":"1997","unstructured":"Kolev, L.: Use of Interval Slopes for the Irrational Part of Factorable Functions, Reliable Com puting 3 (1) (1997), pp. 83\u201393.","journal-title":"Reliable Computing"},{"key":"4875_CR10","unstructured":"Kolev, L. and Filipova-Petrakieva, S.: Outer Bounds on the Eigenvalues of Interval Matrices\u2014The Complex Eigenvalues Case, in: Proc. of the Techn. University\u2014Sofia, 51, 2000\u20132001, pp. 139\u2013147."},{"key":"4875_CR11","unstructured":"Kolev, L., Filipova-Petrakieva, S., and Vrabchev, N.: Outer Bounds on the Real Eigenvalues of Interval Matrices, in: Proc. of the ISTET-2001, Lini, Austria, 19\u201322 August, 2001, pp. 383- 386."},{"key":"4875_CR12","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1109\/TAC.2005.843857","volume":"50","author":"L. Kolev","year":"2005","unstructured":"Kolev, L. and Petrakieva, S.: Assessing the Stability of Linear Time-Invariant Continuous Interval Dynamic Systems, IEEE Transactions on Automatic Control 50 (2005), pp. 393\u2013397.","journal-title":"IEEE Transactions on Automatic Control"},{"key":"4875_CR13","unstructured":"Kolev, L. and Patrakieva, S.: Stability Analysis of Linear Interval Parameter Systems via Assessing the Eigenvalues Range, in: Proc. of the ISTET-2003, 6\u20139 July, 2003, Warsaw, Poland, pp. 211- 215."},{"key":"4875_CR14","doi-asserted-by":"crossref","first-page":"604","DOI":"10.1137\/0722037","volume":"22","author":"R. Krawczyk","year":"1985","unstructured":"Krawczyk, R. and Neumaier, A.: Interval Slopes for Rational Functions and Associated Centered Forms, SIAM J. Numer. Anal 22 (1985), pp. 604\u2013616.","journal-title":"SIAM J. Numer. Anal"},{"key":"4875_CR15","volume-title":"Solving Polynomial Systems Using Continuation for Scientific and Engineering Problems","author":"A. P. Morgan","year":"1987","unstructured":"Morgan, A. P.: Solving Polynomial Systems Using Continuation for Scientific and Engineering Problems, Prentice Hall, Englewood Cliffs, 1987."},{"key":"4875_CR16","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/BF02239750","volume":"42","author":"S. M. Rump","year":"1989","unstructured":"Rump, S. M.: Guaranteed Inclusions for the Complex Generalized Eigenproblem, Computing 42 (1989), pp. 225\u2013238.","journal-title":"Computing"},{"key":"4875_CR17","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1007\/978-94-017-1247-7_7","volume-title":"Developments in Reliable Computing","author":"S. M. Rump","year":"1999","unstructured":"Rump, S. M.: INTLAB\u2014INTerval LABoratory, in: Csendes, T. (ed.), Developments in Reliable Computing, Kluwer Academic Publishers, Dordrecht, 1999, pp. 77\u2013105."},{"key":"4875_CR18","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1023\/B:BITN.0000009941.51707.26","volume":"43","author":"S. M. Rump","year":"2003","unstructured":"Rump, S. M. and Zemke, M.: On Eigenvector Bounds, BIT Numerical Mathematics 43 (2003), pp. 823\u2013837.","journal-title":"BIT Numerical Mathematics"},{"key":"4875_CR19","first-page":"89","volume":"39","author":"S. Zuhe","year":"1990","unstructured":"Zuhe, S. and Wolfe, M. A.: On Interval Enclosures Using Slope Arithmetic, Appl. Math. Comput. 39 (1990), pp. 89\u2013105.","journal-title":"Appl. Math. Comput."}],"container-title":["Reliable Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11155-006-4875-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11155-006-4875-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11155-006-4875-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T08:31:34Z","timestamp":1559377894000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11155-006-4875-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,4]]},"references-count":19,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2006,4]]}},"alternative-id":["4875"],"URL":"https:\/\/doi.org\/10.1007\/s11155-006-4875-1","relation":{},"ISSN":["1385-3139","1573-1340"],"issn-type":[{"value":"1385-3139","type":"print"},{"value":"1573-1340","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,4]]}}}