QUASI-BLOCK TOEPLITZ MATRIX IN MATLAB

QUASI-BLOCK TOEPLITZ MATRIX IN MATLAB

M. SHAMS SOLARY

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Abstract. 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;k2Z, that Fk are m  m matrices such that P i2Z jFij has bounded entries, and E = (ei;j)i;j2Z+ is a compact correction. Also, we should say the norms k F kw= P i2Z k Fi k and k E k2 are finite. QBT-matrices are done with any given precision. The norm k F kQBT =  k F kw + k E k2, is for  = (1 + p 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.

Keywords:Quasi-Block Toeplitz matrix, Banach algebra, Matlab.

AMS Subject Classification: 65F30, 60B20.