TECHNICAL NOTES AND SHORT PAPERS On Optimal Alternating Direction Parameters
نویسنده
چکیده
The iterative process, Xn+i = X„i2I — AX„), for computing A-1, is generalized to obtain the generalized inverse. An iterative method for inverting a matrix, due to Schulz [1], is based on the convergence of the sequence of matrices, defined recursively by (1) Xn+x = X„i21 AX«) (n 0, 1, • • ■ ) to the inverse A~l of A, whenever X0 approximates A"1. In this note the process ( 1 ) is generalized to yield a sequence of matrices converging to A +, the generalized inverse of A [2\. Let A denote an m X n complex matrix, A its conjugate transpose, Pru) the perpendicular projection of Em on the range of A, Pru') the perpendicular projection of En on the range of A*, and A+ the generalized inverse of A. Theorem. The sequence of matrices defined by (2) X.+i = X.(2P.u) AX.) ■ (« = 0, 1, •••), Received November 9, 1964. License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use
منابع مشابه
Technical Notes and Short Papers
By J. Douglas, Jr., R. B. Kellogg, and R. S. Varga We consider the iterative solution of the system of linear equations (1 ) (Xi + X-, + • ■ ■ + Xn)z = /, n 2; 2, where each Xj, 1 | j | n, is a Hermitian and positive definite N X N matrix. If n = 2, the iterative methods of Peaceman-Rachford [1, Chapter 7], or D'yakonov [2] and Kellogg [3], may be used to solve (1). In this paper these methods ...
متن کاملNotes on some remarkable epiphytic lichens from Mazandaran province and a short history of lichenology in the Hyrcanian forest, N Iran
Nineteen species of mostly epiphytic lichens from the forests of Nowshahr and Royan located in Mazandaran province (N Iran) are reported. Three species, Ochrolechia pallescens, Phaeophyscia confusa and Usnea longissima, are newly reported for lichenized mycota of Iran and seven species are new to the province. Additionally, a short history of lichenological exploration in the Hyrcanian forest i...
متن کاملEcography: Pattern and Diversity in Ecology
Ecography publishes four types of articles: -Original research papers present research focused on ecological and geographical patterns in space and time. -Forum papers are commentaries, short papers or notes about new ideas, alternative ways of evaluating existing information or responses to recent papers in Ecography or elsewhere that deal with spatio-temporal issues in ecology. -Review & Synt...
متن کاملEcography: Pattern and Diversity in Ecology
Ecography publishes four types of articles: -Original research papers present research focused on ecological and geographical patterns in space and time. -Forum papers are commentaries, short papers or notes about new ideas, alternative ways of evaluating existing information or responses to recent papers in Ecography or elsewhere that deal with spatio-temporal issues in ecology. -Review & Synt...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010