On solution of two-sided vector equation in tropical algebra

The problem of solving, in the context tropical mathematics, a vector equation with two given matrices and unknown vectors, each part which has form product one an vector, is considered. Such equation, vectors on either side equal sign, often called two-sided equation. A new procedure for solving proposed based minimizing certain distance function between spaces that are generated by columns matrices. As result procedure, pair obtained, provides minimum value itself. If solutions, then resulting solution to Otherwise, these define pseudo-solution minimizes deviation from other. execution consists constructing sequence pseudosolutions left right sides alternately replaced constant vectors. Unlike well known alternation algorithm, corresponding inequalities solved instead equations, uses different argument, looks simpler, allows establish natural criteria completing calculations. no also finds determines error associated it, can be useful approximation problems.