This paper discusses the computational efficiency of the determinant,the matrix inversion and the block matrix inversion.For the multivariable systems with coupled information vectors,we study the subsystem recursive least squares (RLS) identification algorithm and the joint RLS identification agorithm with less computation are studied.For the multivariable systems the partially coupled information vectors,the subsystem least squares identification algorithm and the block matrix inversion based least squares identification algorithm are presented and the subsystem RLS identification algorithm and the identification model decomposition based RLS identification algorithm are proposed.Finally,the comptutational efficiency of the proposed algorithms is analyzed.