منابع مشابه
Rank-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...
متن کاملBlocked rank-revealing QR factorizations: How randomized sampling can be used to avoid single-vector pivoting
Given a matrix A of size m × n, the manuscript describes a algorithm for computing a QR factorization AP = QR where P is a permutation matrix, Q is orthonormal, and R is upper triangular. The algorithm is blocked, to allow it to be implemented efficiently. The need for single vector pivoting in classical algorithms for computing QR factorizations is avoided by the use of randomized sampling to ...
متن کاملSuccessive 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 کاملMultifrontral multithreaded rank-revealing sparse QR factorization
SuiteSparseQR is a sparse multifrontal QR factorization algorithm. Dense matrix methods within each frontal matrix enable the method to obtain high performance on multicore architectures. Parallelism across different frontal matrices is handled with Intel’s Threading Building Blocks library. Rank-detection is performed within each frontal matrix using Heath’s method, which does not require colu...
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: 1987
ISSN: 0024-3795
DOI: 10.1016/0024-3795(87)90103-0