A quasi-Toeplitz (QT) matrix is a semi-infinite of the form \(A=T(a)+E\) where T(a) Toeplitz with entries \((T(a))_{i,j}=a_{j-i}\), for \(a_{j-i}\in \mathbb {C}\), \(i,j\ge 1\), while E representing compact operator in \(\ell ^2\). The finitely representable if \(a_k=0\) \(k<-m\) and \(k>n\), given \(m,n>0\), has finite number nonzero entries. problem numerically computing eigenpairs QT investi...