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.

On the modified Gram-Schmidt algorithm for weighted and constrained linear least squares problems.

Abstract: A framework and an algorithm for using modified Gram-Schmidt for constrained and weighted linear least squares problems is presented. It is shown that a direct implementation of a weighted modified ...

QR methods and error analysis for computing Lyapunov and Sacker---Sell spectral intervals for linear differential-algebraic equations

Abstract: In this paper, we propose and investigate numerical methods based on QR factorization for computing all or some Lyapunov or Sacker---Sell spectral intervals for linear differential-algebraic equations. Furthermore, a perturbation and error analysis for these methods is presented. We investigate how errors in the data and in the numerical integration affect the accuracy of the approximate spectral intervals. Although we need to integrate numerically some differential-algebraic systems on usually very long time-intervals, under certain assumptions, it is shown that the error of the computed spectral intervals can be controlled by the local error of numerical integration and the error in solving the algebraic constraint. Some numerical examples are presented to illustrate the theoretical results.

A note on the direct sum decomposition of two-dimensional behaviors

Abstract: In this paper, the possibility of obtaining certain direct sum decompositions, for a given complete two-dimensional behavior, are investigated and proved to be equivalent to the zero skew-primeness property of suitable matrix pairs. Some known decomposition theorems for two-dimensional complete behaviors are later obtained as simple corollaries of this general result.

An algorithm to compute the polar decomposition of a 3 × 3 matrix

Abstract: We propose an algorithm for computing the polar decomposition of a 3 × 3 real matrix that is based on the connection between orthogonal matrices and quaternions. An important application is to 3D transformations in the level 3 Cascading Style Sheets specification used in web browsers. Our algorithm is numerically reliable and requires fewer arithmetic operations than the alternative of computing the polar decomposition via the singular value decomposition.

Polynomial matrix QR decomposition for the decoding of frequency selective multiple-input multiple-output communication channels

Abstract: This study proposes a new technique for communicating over multiple-input multiple-output (MIMO) frequency selective channels. This approach operates by calculating the QR decomposition of the polynomial channel matrix at the receiver on the basis of channel state information, which in this work is assumed to be perfectly known. This then enables the frequency selective MIMO system to be transformed into a set of frequency selective single-input single-output systems without altering the statistical properties of the receiver noise, which can then be individually equalised. A like-for-like comparison with the orthogonal frequency division multiplexing scheme, which is typically used to communicate over channels of this form, is provided. The polynomial matrix system is shown to achieve improved performance in terms of average bit error rate results, as a consequence of time-domain symbol decoding.