منابع مشابه
Successive Rank-Revealing Cholesky Factorizations on GPUs
We present an algorithm and its GPU implementation for fast generation of rank-revealing Cholesky factors {Rk} at output in response to a sequence of data matrices {Ak} at input. The Cholesky factors are subsequently used for calculating adaptive weight vectors as control feedback in space-time adaptive processing (STAP) and sensing systems [3]. The size of the input data matrices is m× n, wher...
متن کاملStrong Rank Revealing Cholesky Factorization
STRONG RANK REVEALING CHOLESKY FACTORIZATION M. GU AND L. MIRANIAN y Abstract. For any symmetric positive definite n nmatrixAwe introduce a definition of strong rank revealing Cholesky (RRCh) factorization similar to the notion of strong rank revealing QR factorization developed in the joint work of Gu and Eisenstat. There are certain key properties attached to strong RRCh factorization, the im...
متن کاملHigh Resolution Methods Based On Rank Revealing Triangular Factorizations
In this paper, we propose a novel method for subspace estimation used high resolution method without eigendecomposition where the sample Cross-Spectral Matrix (CSM) is replaced by upper triangular matrix obtained from LU factorization. This novel method decreases the computational complexity. The method relies on a recently published result on Rank-Revealing LU (RRLU) factorization. Simulation ...
متن کاملRank-Revealing QR Factorizations and the Singular Value Decomposition
T. Chan has noted that, even when the singular value decomposition of a matrix A is known, it is still not obvious how to find a rank-revealing QR factorization (RRQR) of A if A has numerical rank deficiency. This paper offers a constructive proof of the existence of the RRQR factorization of any matrix A of size m x n with numerical rank r. The bounds derived in this paper that guarantee the e...
متن کاملA randomized algorithm for rank revealing QR factorizations and applications
The basic steps of a RRQR Factorization are: (i) select columns from the input matrix A, (ii) permute them to leading positions to a new matrix Ap, (iii) compute a QR Factorization Ap = QR, (iv) reveal rank(A) from R. Since their introduction [1, 2], algorithmic trends have involved procedures for deterministically selecting columns from A [3, 4, 5]. Motivated by recent results in theoretical c...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2003
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(02)00572-4