Topic
QR decomposition
About: QR decomposition is a research topic. Over the lifetime, 3504 publications have been published within this topic receiving 100599 citations. The topic is also known as: QR factorization.
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TL;DR: The main purpose of this paper is to show that this algorithm is numerically equivalent to the standard QR algorithm, and how this connection may be used to develop a better understanding of the periodic QR algorithm.
19 citations
TL;DR: It is shown that it can be used to prove the existence of max-algebraic analogues of some basic matrix decompositions from linear algebra, including those of the QR decomposition, the singular value decomposition (SVD), the Hessenberg decompose, the LU decomposition and so on.
Abstract: In this paper we discuss matrix decompositions in the symmetrized max-plus algebra. The max-plus algebra has maximization and addition as basic operations. In contrast to linear algebra, many fundamental problems in the max-plus algebra still have to be solved. In this paper we discuss max-algebraic analogues of some basic matrix decompositions from linear algebra. We show that we can use algorithms from linear algebra to prove the existence of max-algebraic analogues of the QR decomposition, the singular value decomposition (SVD), the Hessenberg decomposition, the LU decomposition, and so on.
19 citations
TL;DR: Near perfect load balancing is achieved by exploiting a ‘commutativity’ property of the Kronecker product, and communication requirements are minimized by employing a binary exchange algorithm for matrix transposition.
19 citations
06 Jun 2010
TL;DR: A way of efficiently implementing the tile QR factorization on a system with a powerful GPU and many multicore CPUs is presented.
Abstract: The tile QR factorization provides an efficient and scalable way for factoring a dense matrix in parallel on multicore processors. This article presents a way of efficiently implementing the algorithm on a system with a powerful GPU and many multicore CPUs.
19 citations
TL;DR: This paper takes advantage of the well pseudorandom of chaotic sequence, introduces the concept of the incoherence factor and rotation, and adopts QR decomposition to obtain the IRC measurement matrix which is suited for sparse reconstruction and satisfies the Restricted Isometry Property criterion in sparse reconstruction.
Abstract: Measurement matrix construction is the hot issue of compressed sensing. How to construct a measurement matrix of good performance and easy hardware implementation is the main research problem in compressed sensing. In this paper, we present a novel simple and efficient measurement matrix named Incoherence Rotated Chaotic (IRC) matrix. We take advantage of the well pseudorandom of chaotic sequence, introduce the concept of the incoherence factor and rotation, and adopt QR decomposition to obtain the IRC measurement matrix which is suited for sparse reconstruction. The IRC matrix satisfies the Restricted Isometry Property criterion in sparse reconstruction and has a smaller RIP ratio. Simulations demonstrate IRC matrix has better performance than Gaussian random matrix, Bernoulli random matrix, Fourier matrix and can efficiently work on both natural image and remote sensing image. The peak signal-to-noise ratios of reconstructed images using IRC matrix are improved at 1.5 dB to 2.5 dB at least.
19 citations