how to most efficiently solve equation?

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SpeedyGonzales
SpeedyGonzales 2018-1-13
编辑： Walter Roberson 2018-1-14
Hi, I have the following data (see file attached)
f 8594x93 matrix w 8594x1 vector z 1x93 vector
I want to now find a vector w1 (8594x1) such that w1' * f = z. Asked differently, how does w1 need to look if when multiplied with f gives exactly z?
What is the most efficient way of setting this up in Matlab? Thanks GonzalesSpeedy

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Matt J
Matt J 2018-1-13
编辑：Matt J 2018-1-13
w1= z/f

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SpeedyGonzales
SpeedyGonzales 2018-1-13
thanks. That was easy!
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Roger Stafford
Roger Stafford 2018-1-13
编辑：Walter Roberson 2018-1-14
It is important to realize that your problem is the equivalent of having 93 linear equations in 8594 unknowns. Consequently the solution obtained by z/f will be far from unique. In fact it probably has some 8501 degrees of freedom. Matlab uses a kind of "least-squares" optimization in making its selection out of all these possibilities. See the website:
https://www.mathworks.com/help/matlab/ref/mrdivide.html
Matt J
Matt J 2018-1-14
SpeedyGonzales' comment moved here:
Thank you Roger for your comment. For the time being it is not ultimately important to have the optimal solution, just one that satisfies my conditions suffices.

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