Construction of upper and lower solutions for singular discrete initial and boundary value problems via inequality theory.
Convergence acceleration of shifted transformations for totally nonnegative Hessenberg matrices
We design shifted transformations based on the integrable discrete hungry Toda equation to compute eigenvalues of totally nonnegative matrices of the banded Hessenberg form. The shifted transformation can be regarded as an extension of the extension employed in the well-known dqds algorithm for the symmetric tridiagonal eigenvalue problem. In this paper, we propose a new and effective shift strategy for the sequence of shifted transformations by considering the concept of the Newton shift....