The generalized Schur algorithm (GSA) allows computing well-known matrix decompositions, such as QR and LU factorizations [1]. In particular, if the involved matrix is structured, i.e., Toeplitz, block-Toeplitz or Sylvester, the GSA computes the R factor of the QR factorization with complexity of one order of magnitude less than that of the classical QR algorithm [2], since it relies only on t…