Solution of an eigenvalue problem for pencils of band matrices

An iterative algorithm is proposed for solving the complete eigenvalue problem of a regular, linear pencil $A-\lambda B$ of matrices $A$ and $B$ of band structure which under certain conditions preserves the band structure of matrices of the pencil. It is modification of the algorithm $AB-1$ based on applying nonorthogonal transformations. A detailed description of the algorithm is presented in application to the pencils with tridiagonal and pentadiagonal matrices.