نتایج جستجو برای: gram schmidt orthogonalization process

تعداد نتایج: 1384767  

Journal: :IEICE Transactions 2011
Yuyuan Chang Kiyomichi Araki

In multiple-input multiple-output (MIMO) systems, the multiuser MIMO (MU-MIMO) systems have the potential to provide higher channel capacity owing to multiuser and spatial diversity. Block diagonalization (BD) is one of the techniques to realize MU-MIMO systems, where multiuser interference can be completely cancelled and therefore several users can be supported simultaneously. When the number ...

Journal: :CoRR 2013
Zhaocheng Yang Rodrigo C. de Lamare Xiang Li Hongqiang Wang

This paper presents knowledge-aided space-time adaptive processing (KA-STAP) algorithms that exploit the lowrank dominant clutter and the array geometry properties (LRGP) for airborne radar applications. The core idea is to exploit the fact that the clutter subspace is only determined by the spacetime steering vectors, redwhere the Gram-Schmidt orthogonalization approach is employed to compute ...

2007
Ali Akhavi Jean-François Marckert Alain Rouault

For g < n, let b1, . . . , bn−g be n− g independent vectors in R with a common distribution invariant by rotation. Considering these vectors as a basis for the Euclidean lattice they generate, the aim of this paper is to provide asymptotic results when n → +∞ concerning the property that such a random basis is reduced in the sense of Lenstra, Lenstra & Lovász. The proof passes by the study of t...

Journal: :SIAM Journal on Scientific Computing 2022

A randomized Gram--Schmidt algorithm is developed for orthonormalization of high-dimensional vectors or QR factorization. The proposed process can be less computationally expensive than the classical while being at least as numerically stable modified process. Our approach based on random sketching, which a dimension reduction technique consisting in estimation inner products by their small eff...

Journal: :Proceedings in applied mathematics & mechanics 2023

Mixed precision hardware has recently become commercially available, and more than 25% of the supercomputers in TOP500 list now have mixed capabilities. Using lower algorithms can be beneficial terms reducing both computation communication costs. There are many current efforts towards developing numerical linear algebra algorithms, which lead to speedups real applications. Motivated by this, we...

2002
Nobuhiro Asai Izumi Kubo

Let μ be a probability measure on the real line with finite moments of all orders. Apply the Gram-Schmidt orthogonalization process to the system {1, x, x, . . . , xn, . . . } to get orthogonal polynomials Pn(x), n ≥ 0, which have leading coefficient 1 and satisfy (x − αn)Pn(x) = Pn+1(x) + ωnPn−1(x). In general it is almost impossible to use this process to compute the explicit form of these po...

Journal: :IACR Cryptology ePrint Archive 2015
Vadim Lyubashevsky Thomas Prest

A procedure for sampling lattice vectors is at the heart of many lattice constructions, and the algorithm of Klein (SODA 2000) and Gentry, Peikert, Vaikuntanathan (STOC 2008) is currently the one that produces the shortest vectors. But due to the fact that its most time-efficient (quadratic-time) variant requires the storage of the GramSchmidt basis, the asymptotic space requirements of this al...

Journal: :International Journal of Advanced Research in Artificial Intelligence 2015

1998
Thomas E. Biedka

Many blind adaptive beamforming algorithms require the selection of one or more non-zero initial weight vectors. Proper selection of the initial weight vectors can speed algorithm convergence and help ensure convergence to the desired solutions. Three alternative initialization approaches are compared here, all of which depend only on second order statistics of the observed data. These methods ...

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