Name of the matrix: block quasiseparable matrix of order $(n_1,n_2)$ with block entries $R_{i,j}$, $1\leq i,j\leq N$, of size $m$

Pattern:

$$R_{i,j}=\left\{\begin{array}{ccccc}P_i A_{i+1}\cdots A_{j-1} Q_j ... ...1}\cdots B_{j+1} H_j\ {\rm for } \ 1< j+1 \leq i-1 < N, \end{array}\right.$$

where $P_i\in \mathbb{C}^{m\times n_1}$, $Q_i\in \mathbb{C}^{n_1\times m}$, $A_i\in \mathbb{C}^{n_1\times n_1}$, $D_i\in \mathbb{C}^{m\times m}$, $G_i\in \mathbb{C}^{m\times n_2}$, $H_i\in \mathbb{C}^{n_2\times m}$, $B_i\in \mathbb{C}^{n_2\times n_2}$.

Properties: principal off-diagonal submatrices of low rank, unified description for the structure of band matrices and inverses of band matrices

Source/utilization: test for linear system solvers and for the computation of the eigenvalues

References Y. Eidelman and I. Gohberg, Integral Equations and Operator Theory, 34(1999), 293-324