The periodic QR algorithm is a disguised QR algorithm
نویسندگان
چکیده
منابع مشابه
The Periodic QR Algorithm is a Disguised QR Algorithm
Abstract The periodic QR algorithm is a strongly backward stable method for computing the eigenvalues of products of matrices, or equivalently for computing the eigenvalues of block cyclic matrices. The main purpose of this paper is to show that this algorithm is numerically equivalent to the standard QR algorithm. It will be demonstrated how this connection may be used to develop a better unde...
متن کاملQR algorithm
A = PUP∗, where P∗P = I and U is upper triangular, then the eigenvalues of A are given by the diagonal elements of U. The QR method developed by Francis in 1960’s [4] is classified as one of the topten developments in computation in the 20th century. The performance and robustness is still actively improved within the numerical linear algebra research community. We will now introduce the QR-met...
متن کاملThe QR Algorithm
5 Some Techniques to accelerate convergence in the QR algorithm 8 5.1 Deflation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5.2 The Wilkinson shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5.3 Obtaining the eigenvectors . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5.4 Ad hoc shifts . . . . . . . . . . . . . . . . . . . . . . . . . . ...
متن کاملThe QR Algorithm Revisited
The QR algorithm is still one of the most important methods for computing eigenvalues and eigenvectors of matrices. Most discussions of the QR algorithm begin with a very basic version and move by steps toward the versions of the algorithm that are actually used. This paper outlines a pedagogical path that leads directly to the implicit multishift QR algorithms that are used in practice, bypass...
متن کاملThe QR algorithm
A brief sketch of the early days of eigenvalue hunting is followed by a description of the QR algorithm and its major virtues. The symmetric case brings with it guaranteed convergence and an elegant implementation. An account of the impressive discovery of the algorithm brings the essay to a close.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2006
ISSN: 0024-3795
DOI: 10.1016/j.laa.2003.06.014