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When calculating least-squares we use the form $Xw=y$ This gives us an approximation, and it can happen that the resulting $w$ will be such that $Xw \lt y$ (entry-wise).

Is there a way how to make every entry in $w$ big enough so that $Xw \ge y$?

And is it possible, at the same time, to make sure every entry in $Xw$ is less that some other number?

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    Hello,I think yes. Please excuse me, I am not good at maths and definitions, but I try to explain a bit more what I'd like to calculate. for example: I have Matrix$X$m*n(5x4), vector$y$(y1,y2,y3,y4,y5) and vector$z$(z1,z2,z3,z4,z5), their values are given. I need to find such (only one vector)$w$(w1,w2,w3,w4,w5) with the smallest error, in relation to the vector y, that: y1<= Xm1n1*w1 + Xm2n1*w2 + Xm3n1*w3 + Xm4n1*w4 + Xm5n1*w5 < z1 . . . y5<= Xm1n5*w1 + Xm2n5*w2 + Xm3n5*w3 + Xm4n5*w4 + Xm5n5*w5 < z5 .Also, the vector$w$must have positive values. Many thanks for your time. hugo2012-04-09

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