In this paper we try to approximate any properties of quasi-block Toeplitz matrix (QBT), by means of a finite number of parameters. A quasi-block Toeplitz (QBT) matrix is a semi-infinite block matrix of the kind F = T(F) + E where T(F) = (Fj?k)j,k?Z, that Fk are m × m matrices such that ?i?Z|Fi| has bounded entries, and E = (ei,j )i,j?Z+ is a compact correction. Also, we should say the norms ? F ?w= ?i?Z ? Fi ? and ? E ?2 are finite. QBT-matrices are done with any given precision. The norm ? F ?QBT = ? ? F ?w + ? E ?2, is for ? = (1 + ?5)/2. These matrices are a Banach algebra with the standard arithmetic operations. We try to analysis some structures and computational properties for arithmetic operations of QBT matrices with some MATLAB commands. Publisher's Version