{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,2]],"date-time":"2023-04-02T12:09:52Z","timestamp":1680437392726},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2009,2,27]],"date-time":"2009-02-27T00:00:00Z","timestamp":1235692800000},"content-version":"unspecified","delay-in-days":5020,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["AIEDAM"],"published-print":{"date-parts":[[1995,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper defines, develops algorithms for, and illustrates the utility in design of a class of mathematical operations. These accept as inputs a system of linear constraint equations, <jats:bold>Ax = b<\/jats:bold>, an interval matrix of values for the coefficients, <jats:bold>A<\/jats:bold>, and an interval vector of values for either <jats:bold>x<\/jats:bold> or <jats:bold>b<\/jats:bold>. They return a set of values for the \u201cdomain\u201d of the other vector, in the sense that all combinations of the output vector values set and values for <jats:bold>A<\/jats:bold>, when inserted into the constraint equation, correspond to values for the input vector that lie within the input interval. These operations have been mostly overlooked by the interval matrix arithmetic community, but are mathematically interesting and useful in the design, for example, of structures.<\/jats:p>","DOI":"10.1017\/s0890060400002432","type":"journal-article","created":{"date-parts":[[2010,3,31]],"date-time":"2010-03-31T13:46:29Z","timestamp":1270043189000},"page":"197-210","source":"Crossref","is-referenced-by-count":2,"title":["The DOMAIN family of propagation operations for intervals on simultaneous linear equations"],"prefix":"10.1017","volume":"9","author":[{"given":"R.","family":"Chen","sequence":"first","affiliation":[]},{"given":"A.C.","family":"Ward","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2009,2,27]]},"reference":[{"key":"S0890060400002432_ref010","unstructured":"Ly T.E.A. , & Girczyc E.F. (1988). Constraint propagation in an object-oriented IC design environment. 25th ACM\/IEEE Design Automation Conference, pp. 628\u2013633."},{"key":"S0890060400002432_ref009","doi-asserted-by":"publisher","DOI":"10.1007\/BF02238739"},{"key":"S0890060400002432_ref007","first-page":"308","article-title":"Interval arithmetic in matrix computations, Part I","volume":"2","author":"Hansen","year":"1965","journal-title":"SIAM J. Numerical Analysis"},{"key":"S0890060400002432_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-82739-6"},{"key":"S0890060400002432_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/0004-3702(87)90091-9"},{"key":"S0890060400002432_ref003","unstructured":"Chang T.-S. , Ward A. , Lee J. , & Jacox E. Conceptual robustness in simultaneous engineering: An extension of Taguchi\u2019s parameter design. Research in Engineering Design (in press)."},{"key":"S0890060400002432_ref012","volume-title":"Interval Analysis","author":"Moore","year":"1966"},{"key":"S0890060400002432_ref002","doi-asserted-by":"publisher","DOI":"10.1109\/20.106439"},{"key":"S0890060400002432_ref001","volume-title":"Introduction to Interval Computation","author":"Alefeld","year":"1983"},{"key":"S0890060400002432_ref011","doi-asserted-by":"publisher","DOI":"10.1109\/59.49103"},{"key":"S0890060400002432_ref004","unstructured":"Chen R. , & Ward A. The \u2018range\u2019 family of propagation operations for intervals on simultaneous linear equations. AI EDAM (in press)."},{"key":"S0890060400002432_ref008","first-page":"279","volume-title":"ASME Design Theory and Methodology Conference","author":"Habib","year":"1991"}],"container-title":["Artificial Intelligence for Engineering Design, Analysis and Manufacturing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0890060400002432","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,13]],"date-time":"2019-05-13T21:42:29Z","timestamp":1557783749000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0890060400002432\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,6]]},"references-count":12,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1995,6]]}},"alternative-id":["S0890060400002432"],"URL":"https:\/\/doi.org\/10.1017\/s0890060400002432","relation":{},"ISSN":["0890-0604","1469-1760"],"issn-type":[{"value":"0890-0604","type":"print"},{"value":"1469-1760","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,6]]}}}