A not sign-preserving iteration algorithm for the ‘Improved Normalized Squared Differences’ matrix adjustment model

Abstract Estimating the elements of a matrix, when only margins (row and column sums) are known, but supposedly similar ‘reference matrix’ is available, standard problem in many disciplines. After discussing main types, issues applications these two-directional matrix adjustment problems paper concentrates on case negative models with quadratic objective functions. The solution Improved Normalized Squared Differences (INSD) model proved to be same as result that iteration algorithm which presented paper. It also argued if sign-preservation requirement dropped then procedure suggested by Huang et al. (Econ Syst Res 20(1):111–123, 2008) boils down algorithm. Using numerical example earlier literature it demonstrated even this not sign-preserving case, requires sign-flips for some elements, INSD-model produces good fit mathematical terms.