The unitary completion and QR iterations for a class of structured matrices
نویسندگان
چکیده
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.
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عنوان ژورنال:
- Math. Comput.
دوره 77 شماره
صفحات -
تاریخ انتشار 2008