Our work is concerned with the derivation of systolic arrays for certain Toeplitz linear systems of equations. First, the notion of Toeplitz systems is presented. Then, the solution of tridiagonal systems of equations is discussed. It is based on aQQTfactorisation, whereQis an upper bidiagonal rectangular Toeplitz matrix. Next, the algorithm for solving a tridiagonal system of equations is analysed. The single assignment code algorithms arc derived and the broadcast of data is removed. The data dependence method is used for mapping algorithms into systolic arrays.