A new real structure-preserving quaternion 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...
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In this paper we propose a fast structure-preserving algorithm for computing the singular value decomposition of quaternion matrices. The algorithm is based on the structurepreserving bidiagonalization of the real counterpart for quaternion matrices by applying orthogonal JRS-symplectic matrices. The algorithm is efficient and numerically stable. 2014 Elsevier Inc. All rights reserved.
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چکیده ندارد.
15 صفحه اولThe 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 . . . . . . . . . . . . . . . . . . . . . . . . . . ...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2018
ISSN: 0377-0427
DOI: 10.1016/j.cam.2018.04.019