On nonnegative solutions of random systems of linear inequalities
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چکیده
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on the effect of linear & non-linear texts on students comprehension and recalling
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15 صفحه اولOn 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...
متن کاملSparse Solutions to Nonnegative Linear Systems and Applications
We give an efficient algorithm for finding sparse approximate solutions to linear systems of equations with nonnegative coefficients. Unlike most known results for sparse recovery, we do not require any assumption on the matrix other than non-negativity. Our algorithm is combinatorial in nature, inspired by techniques for the set cover problem, as well as the multiplicative weight update method...
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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: Discrete & Computational Geometry
سال: 1987
ISSN: 0179-5376,1432-0444
DOI: 10.1007/bf02187872