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: Two new techniques for obtaining the Q factor in the QR factorization of some (or all) columns of a fundamental solution matrix Y of a linear differential system based on elementary Householder and Givens transformations are introduced and analyzed.
Abstract: In this work, we introduce and analyze two new techniques for obtaining the Q factor in the QR factorization of some (or all) columns of a fundamental solution matrix Y of a linear differential system. These techniques are based on elementary Householder and Givens transformations. We implement and compare these new techniques with existing approaches on some examples.
33 citations
TL;DR: A version of this type of algorithm based on the orthogonal triangular factorization technique known as the QR decomposition is presented and its computational complexity and numerical properties are briefly discussed.
33 citations
TL;DR: A very low-complexity maximum-likelihood detection algorithm based on QR decomposition for the quasi-orthogonal space-time block code (QSTBC) with four transmit antennas, called the LC-ML decoder, enables the QSTBC to achieve ML performance with significant reduction in computational load for any high-level modulation scheme.
Abstract: This letter proposes a very low-complexity maximum-likelihood (ML) detection algorithm based on QR decomposition for the quasi-orthogonal space-time block code (QSTBC) with four transmit antennas, called the LC-ML decoder. The proposed algorithm enables the QSTBC to achieve ML performance with significant reduction in computational load for any high-level modulation scheme.
33 citations
TL;DR: In this paper, a new method for computing all the Lyapunov characteristic exponents (LCEs) of n-dimensional continuous dynamical systems is presented, which relies on the use of the Cayley Transform and a development of the ability to restart the computations for the variational equation.
Abstract: A new method for computing all the Lyapunov characteristic exponents (LCEs) of n-dimensional continuous dynamical systems is presented. The method relies on the use of the Cayley Transform and a development of the ability to restart the computations for the variational equation. The method intrinsically maintains the orthogonality of the Q matrix in the QR decomposition of the solution of the variational equation. It therefore does not suffer from the type of computational breakdown that occurs with the standard method for computing LCEs. An example of a Lorenz system showing the breakdown of the standard method is presented, and the same example is used to compute the LCEs by the present method. Comparisons of the computational efficiency of the proposed method in relation to the standard method, and the standard-method-with-reorthogonalization are presented. Issues of accuracy are addressed.
33 citations
TL;DR: The redistributed invariant integer wavelet transform is proposed, which has real reversibility and can transform an image into the invariant domain where the pixel values are all integers, and a new method for finding the singular value of an image matrix by QR decomposition and singular value decomposition is given.
33 citations