The unitary completion and QR iterations for a class of structured matrices
Dario A. Bini, Yuli Eidelman, Luca Gemignani, I. Gohberg · Mathematics of Computation · 2007
We consider the problem of completion of a matrix with a specified lower triangular part to a unitary matrix. In this paper we obtain the necessary and sufficient conditions of existence of a unitary completion without any additional constraints and give a general formula for this completion. The paper is mainly focused on matrices with the specified lower triangular part of a special form. For such a specified part the unitary completion is a structured matrix, and we derive in this paper the formulas for its structure. Next we apply the unitary completion method to the solution of the eigenvalue problem for a class of structured matrices via structured QR iterations.