Let's say I have
where $a,b,c \geqslant 0$
What's the best way to find solutions for a, b and c so that the results of the sums are as close as possible to the terms on the right-hand side? My method has been a brute-force search but maybe there's a better way. I tagged this with 'matrices' because I didn't know what else to tag it with.
I've also thought about trying to find the variance of the variances to determine a best fit.