Semi-infinite quasi-Toeplitz matrices with applications to QBD stochastic processes
Dario A. Bini, Stefano Massei, Beatrice Meini · Mathematics of Computation · 2017
Denote by W 1 \mathcal {W}_1 the set of complex valued functions of the form a ( z ) = ∑ i = − ∞ + ∞ a i z i a(z)=\sum _{i=-\infty }^{+\infty }a_iz^i such that ∑ i = − ∞ + ∞ | i a i | > ∞ \sum _{i=-\infty }^{+\infty }|ia_i|>\infty . We call QT-matrix a quasi-Toeplitz matrix A A , associated with a symbol a ( z ) ∈ W 1 a(z)\in \mathcal W_1 , of the form A = T ( a ) + E A=T(a)+E , where T ( a ) = ( t i , j )