Hi,
I have an m x n matrix. The row sums and column sums are all fixed (thus, there are m+n constraints). I am free to vary each cell's value as I choose [let's call each cells value x(i,j)]--thus there are m x n parameters. I must minimize the total error. I define the total error as the square of the difference between x(i,j) and a target fixed value f(i,j), where each cell (i,j) has its own target fixed value. The total error would thus be the sum of each of the squared error values. How might I approach such a problem? I can provide clarification if necessary. Thank you!
I have an m x n matrix. The row sums and column sums are all fixed (thus, there are m+n constraints). I am free to vary each cell's value as I choose [let's call each cells value x(i,j)]--thus there are m x n parameters. I must minimize the total error. I define the total error as the square of the difference between x(i,j) and a target fixed value f(i,j), where each cell (i,j) has its own target fixed value. The total error would thus be the sum of each of the squared error values. How might I approach such a problem? I can provide clarification if necessary. Thank you!