On approximate solutions of systems of linear inequalities
نویسندگان
چکیده
منابع مشابه
On Approximate Solutions of Systems of Linear Inequalities
(briefly, -4x^6), one arrives at a vector JC that "almost" satisfies (1). It is almost obvious geometrically that, if (1) is consistent, one can infer that there is a solution x0 of (1) "close" to x. The purpose of this report is to justify and formulate precisely this assertion. We shall use fairly general definitions of functions that measure the size of vectors, since it may be possible to o...
متن کاملOn Approximate Solutions of Systems of Linear Inequalities
Let ~x ~ b be a. consis tent system of linp,ar inequal ities. The principal result is a quantitative formulatIOn of the fa ct t hat if x "almost " sa t isfi es the inequalit ies t hen x is "close" to a solut ion. It is fur ther shown how i t is possible in certain cases to e~timate the $ize of the vector joining x to the nearest solu t ion from the magn itude of t he posit ive coordi nates of A...
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چکیده ندارد.
15 صفحه اولExact and approximate solutions of fuzzy LR linear systems: New algorithms using a least squares model and the ABS approach
We present a methodology for characterization and an approach for computing the solutions of fuzzy linear systems with LR fuzzy variables. As solutions, notions of exact and approximate solutions are considered. We transform the fuzzy linear system into a corresponding linear crisp system and a constrained least squares problem. If the corresponding crisp system is incompatible, then the fuzzy ...
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Article history: Available online 25 March 2011 Submitted by J.J. Loiseau AMS classification: 15A80 15A39 15A03
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ژورنال
عنوان ژورنال: Journal of Research of the National Bureau of Standards
سال: 1952
ISSN: 0091-0635
DOI: 10.6028/jres.049.027