{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T07:52:54Z","timestamp":1771573974510,"version":"3.50.1"},"reference-count":36,"publisher":"Elsevier BV","issue":"2","license":[{"start":{"date-parts":[[1987,6,1]],"date-time":"1987-06-01T00:00:00Z","timestamp":549504000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[1987,6,1]],"date-time":"1987-06-01T00:00:00Z","timestamp":549504000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2005,6,30]],"date-time":"2005-06-30T00:00:00Z","timestamp":1120089600000},"content-version":"vor","delay-in-days":6604,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Complexity"],"published-print":{"date-parts":[[1987,6]]},"DOI":"10.1016\/0885-064x(87)90027-6","type":"journal-article","created":{"date-parts":[[2004,11,6]],"date-time":"2004-11-06T13:01:23Z","timestamp":1099746083000},"page":"201-229","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":27,"title":["The geometry of III-conditioning"],"prefix":"10.1016","volume":"3","author":[{"given":"James W","family":"Demmel","sequence":"first","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/0885-064X(87)90027-6_BIB1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1070\/RM1971v026n02ABEH003827","article-title":"On matrices depending on parameters","volume":"26","author":"Arnold","year":"1971","journal-title":"Russian Math. Surveys"},{"key":"10.1016\/0885-064X(87)90027-6_BIB2","article-title":"Probabilistic Error Analysis of Floating Point and CRD Arithmetics","author":"Bareiss","year":"1981","journal-title":"Department of Electrical Engineering and Computer Science, Northwestern University, Report 81-02-NAM-1"},{"key":"10.1016\/0885-064X(87)90027-6_BIB3","article-title":"A Numerical Analysts's Jordan Canonical Form","author":"Demmel","year":"1983"},{"key":"10.1016\/0885-064X(87)90027-6_BIB4","article-title":"On condition numbers and the distance to the nearest ill-posed problem","author":"Demmel","year":"1986","journal-title":"Numer. Math."},{"key":"10.1016\/0885-064X(87)90027-6_BIB5","article-title":"The Probability That a Numerical Analysis Problem is Difficult","author":"Demmel","year":"1987"},{"key":"10.1016\/0885-064X(87)90027-6_BIB6","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/BF02288367","article-title":"The approximation of one matrix by another of lower rank","volume":"1","author":"Eckart","year":"1936","journal-title":"Psychometrika"},{"key":"10.1016\/0885-064X(87)90027-6_BIB7","doi-asserted-by":"crossref","first-page":"757","DOI":"10.4153\/CMB-1966-083-2","article-title":"Numerical linear algebra","volume":"9","author":"Kahan","year":"1966","journal-title":"Canad. Math. Bull."},{"key":"10.1016\/0885-064X(87)90027-6_BIB8","first-page":"303","article-title":"An estimate for the volume of a tube about a complex hypersurface","volume":"39","author":"Gray","year":"1982","journal-title":"Tensor (N.S.)"},{"issue":"2","key":"10.1016\/0885-064X(87)90027-6_BIB9","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/0040-9383(82)90005-2","article-title":"Comparison theorems for the volumes of tubes as generalizations of the Weyl tube formula","volume":"21","author":"Gray","year":"1982","journal-title":"Topology"},{"key":"10.1016\/0885-064X(87)90027-6_BIB10","series-title":"Matrix Computations","author":"Golub","year":"1983"},{"issue":"3","key":"10.1016\/0885-064X(87)90027-6_BIB11","first-page":"427","article-title":"Complex differential and integral geometry and curvature integrals associated to singularities of complex analytic varieties","volume":"45","author":"Griffiths Phillip","year":"1978","journal-title":"Duke Math. J."},{"issue":"8","key":"10.1016\/0885-064X(87)90027-6_BIB12","doi-asserted-by":"crossref","first-page":"1609","DOI":"10.1002\/j.1538-7305.1970.tb04281.x","article-title":"On the distribution of numbers","volume":"49","author":"Hamming","year":"1970","journal-title":"Bell System Tech. J."},{"key":"10.1016\/0885-064X(87)90027-6_BIB13","doi-asserted-by":"crossref","first-page":"440","DOI":"10.2307\/2371512","article-title":"Tubes and spheres in n-spaces, and a class of statistical problems","volume":"61","author":"Hotelling","year":"1939","journal-title":"Amer. J. Math."},{"key":"10.1016\/0885-064X(87)90027-6_BIB14","doi-asserted-by":"crossref","DOI":"10.21236\/ADA040476","article-title":"Explaining and Ameliorating the Ill Condition of Zeros of Polynomials","author":"Hough","year":"1977"},{"key":"10.1016\/0885-064X(87)90027-6_BIB15","article-title":"Conserving Confluence Curbs III-Condition","author":"Kahan","year":"1972"},{"key":"10.1016\/0885-064X(87)90027-6_BIB16","article-title":"Perturbation Theory for Linear Operators","author":"Kato","year":"1966"},{"key":"10.1016\/0885-064X(87)90027-6_BIB17","series-title":"Elementary Algebraic Geometry","author":"Kendig","year":"1977"},{"key":"10.1016\/0885-064X(87)90027-6_BIB18","volume":"Vol. 2","author":"Knuth","year":"1969"},{"key":"10.1016\/0885-064X(87)90027-6_BIB19","article-title":"Statistical Complexity of Numerical Linear Algebra","author":"Kostlan","year":"1985"},{"key":"10.1016\/0885-064X(87)90027-6_BIB20","series-title":"Fonctions plurisousharmoniques et formes differentieles positive","author":"Lelong","year":"1968"},{"key":"10.1016\/0885-064X(87)90027-6_BIB21","series-title":"On the Volume of Tubes about a Real Variety","author":"Ocneanu","year":"1985"},{"key":"10.1016\/0885-064X(87)90027-6_BIB22","unstructured":"Ocneanu A. On the loss of precision in solving large linear systems to appear"},{"key":"10.1016\/0885-064X(87)90027-6_BIB23","doi-asserted-by":"crossref","DOI":"10.1287\/moor.12.1.121","article-title":"On the efficiency of Newton's method in approximating all zeros of system of complex polynomials","author":"Renegar","year":"1987","journal-title":"Math. Oper. Res."},{"key":"10.1016\/0885-064X(87)90027-6_BIB24","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/BF02165660","article-title":"Properties of a matrix with a very ill-conditioned eigenproblem","volume":"15","author":"Ruhe","year":"1970","journal-title":"Numer. Math."},{"key":"10.1016\/0885-064X(87)90027-6_BIB25","article-title":"Integral Geometry and Geometric Probability","volume":"Vol. 1","author":"Santal\u00f3Luis","year":"1976"},{"issue":"No 1","key":"10.1016\/0885-064X(87)90027-6_BIB26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0273-0979-1981-14858-8","article-title":"The fundamental theorem of algebra and complexity theory","volume":"4","author":"Smale","year":"1981","journal-title":"Bull. Amer. Math. Sac. (N.S.)"},{"key":"10.1016\/0885-064X(87)90027-6_BIB27","series-title":"presented at the International Congress of Mathematics","article-title":"Algorithms for solving equations","author":"Smale","year":"1986"},{"issue":"No. 4","key":"10.1016\/0885-064X(87)90027-6_BIB28","doi-asserted-by":"crossref","first-page":"752","DOI":"10.1137\/1015095","article-title":"Error and perturbation bounds for subspaces associated with certain eigenvalue problems","volume":"15","author":"Stewart","year":"1973","journal-title":"SIAM Rev."},{"key":"10.1016\/0885-064X(87)90027-6_BIB29","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1007\/BF01351593","article-title":"The Lelong number of points of a complex analytic set","volume":"172","author":"This","year":"1967","journal-title":"Math. Ann."},{"key":"10.1016\/0885-064X(87)90027-6_BIB30","volume":"Vol. 1","author":"Van Der Waerden","year":"1953"},{"key":"10.1016\/0885-064X(87)90027-6_BIB31","doi-asserted-by":"crossref","first-page":"461","DOI":"10.2307\/2371513","article-title":"On the volume of tubes","volume":"61","author":"Weyl","year":"1939","journal-title":"Amer. J. Math."},{"key":"10.1016\/0885-064X(87)90027-6_BIB32","series-title":"Rounding Errors in Algebraic Processes","author":"Wilkinson","year":"1963"},{"key":"10.1016\/0885-064X(87)90027-6_BIB33","series-title":"The Algebraic Eigenvalue Problem","author":"Wilkinson","year":"1965"},{"key":"10.1016\/0885-064X(87)90027-6_BIB34","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1007\/BF01402528","article-title":"Note on matrices with a very ill-conditioned eigen-problem","volume":"19","author":"Wilkinson","year":"1972","journal-title":"Numer. Math."},{"key":"10.1016\/0885-064X(87)90027-6_BIB35","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01389751","article-title":"On neighboring matrices with quadratic elementary divisors","volume":"44","author":"Wilkinson","year":"1984","journal-title":"Numer. Math."},{"key":"10.1016\/0885-064X(87)90027-6_BIB36","first-page":"5","article-title":"Sensitivity of eigenvalues","volume":"25","author":"Wilkinson","year":"1984","journal-title":"Utilitas Math."}],"container-title":["Journal of Complexity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:0885064X87900276?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:0885064X87900276?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,9,10]],"date-time":"2025-09-10T14:53:39Z","timestamp":1757516019000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/0885064X87900276"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1987,6]]},"references-count":36,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1987,6]]}},"alternative-id":["0885064X87900276"],"URL":"https:\/\/doi.org\/10.1016\/0885-064x(87)90027-6","relation":{},"ISSN":["0885-064X"],"issn-type":[{"value":"0885-064X","type":"print"}],"subject":[],"published":{"date-parts":[[1987,6]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"The geometry of III-conditioning","name":"articletitle","label":"Article Title"},{"value":"Journal of Complexity","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/0885-064X(87)90027-6","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"converted-article","name":"content_type","label":"Content Type"},{"value":"Copyright \u00a9 1987 Published by Elsevier Inc.","name":"copyright","label":"Copyright"}]}}