Enhancing the distance minimization methods of matrix updating within a homothetic paradigm

1 An introduction to the matrix‐updating problems A general problem of updating rectangular (or square) matrix can be formulated as follows. Let A be an initial matrix of dimension N × M with row and column marginal totals uA = AeM, v A = e ′ NA where eN and eM are N × 1 and M × 1 summation column vectors with unit elements. Further, let u �= uA and v �= vA be exogenous column vectors of dimension N × 1 and M × 1, respectively. The problem is to estimate a target matrix X of dimension N × M at the highest possible level of its structural similarity (or resemblance, likeness, closeness, etc.) to initial matrix A subject to N + M equality constraints Abstract