{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,2]],"date-time":"2023-04-02T12:17:48Z","timestamp":1680437868594},"reference-count":9,"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 design use of a class of mathematical operations. These operations 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 other variable that is \u201csufficient\u201d in this sense. Suppose that \u25ef is an interval of input vectors, and \u00c2 an interval matrix. Then, one Sufficient-Points operation returns a set of vectors ~ such that for each b in ~, the set of x values that can be produced by inserting all the values of \u00c2 into <jats:bold>Ax = b<\/jats:bold> is a superset of the input vector <jats:bold>x<\/jats:bold>. These operations have been partly overlooked by the interval matrix mathematics community, but are mathematically interesting and useful in the design, for example, of circuits.<\/jats:p>","DOI":"10.1017\/s0890060400002444","type":"journal-article","created":{"date-parts":[[2010,3,31]],"date-time":"2010-03-31T09:46:29Z","timestamp":1270028789000},"page":"211-217","source":"Crossref","is-referenced-by-count":2,"title":["The SUFFICIENT-POINTS 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":"S0890060400002444_ref009","first-page":"89","volume-title":"Proceedings of the First International ASME Conference on Design Theory and Methodology","author":"Ward","year":"1989"},{"key":"S0890060400002444_ref007","first-page":"188","article-title":"\u00dcber Gleichungen und \u00fcber L\u00f6sungen","volume":"52","author":"Nuding","year":"1972","journal-title":"ZAMM"},{"key":"S0890060400002444_ref006","first-page":"279","volume-title":"1991 ASME DTM Conference","author":"Habib","year":"1991"},{"key":"S0890060400002444_ref005","first-page":"231","article-title":"Extending generalized interval propagation to monotonic relations among more than three variables","volume":"9","author":"Finch","journal-title":"AI EDAM"},{"key":"S0890060400002444_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-82739-6"},{"key":"S0890060400002444_ref003","first-page":"197","article-title":"The DOMAIN family of set-propagation operations for systems of linear equations","volume":"9","author":"Chen","year":"1995","journal-title":"AI EDAM"},{"key":"S0890060400002444_ref001","unstructured":"Bains N. , & Ward A. Multiple-type interval propagations through non-monotonic equations. ASME Journal of Mechanical Design (in press)."},{"key":"S0890060400002444_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/BF01386090"},{"key":"S0890060400002444_ref002","first-page":"183","article-title":"The RANGE family of propagation operations for intervals on simultaneous linear equations","volume":"9","author":"Chen","year":"1995","journal-title":"AI EDAM"}],"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\/S0890060400002444","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,13]],"date-time":"2019-05-13T17:42:45Z","timestamp":1557769365000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0890060400002444\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,6]]},"references-count":9,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1995,6]]}},"alternative-id":["S0890060400002444"],"URL":"https:\/\/doi.org\/10.1017\/s0890060400002444","relation":{},"ISSN":["0890-0604","1469-1760"],"issn-type":[{"value":"0890-0604","type":"print"},{"value":"1469-1760","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,6]]}}}