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.

Using the Hessenberg decomposition in control theory

Abstract: Orthogonal matrix techniques are gaining wide acceptance in applied areas by practitioners who appreciate the value of reliable numerical software. Quality programs that can be used to compute the QR Decomposition, the Singular Value Decomposition, and the Schur Decomposition are primarily responsible for this increased appreciation. A fourth orthogonal matrix decomposition, the Hessenberg Decomposition, has recently been put to good use in certain control theory applications. We describe some of these applications and illustrate why this decomposition can frequently replace the much more costly decomposition of Schur.

Optimizing polynomial solvers for minimal geometry problems

Abstract: In recent years polynomial solvers based on algebraic geometry techniques, and specifically the action matrix method, have become popular for solving minimal problems in computer vision. In this paper we develop a new method for reducing the computational time and improving numerical stability of algorithms using this method. To achieve this, we propose and prove a set of algebraic conditions which allow us to reduce the size of the elimination template (polynomial coefficient matrix), which leads to faster LU or QR decomposition. Our technique is generic and has potential to improve performance of many solvers that use the action matrix method. We demonstrate the approach on specific examples, including an image stitching algorithm where computation time is halved and single precision arithmetic can be used.

Method and system for determining a signal vector

Abstract: A method for determining a signal vector comprising a plurality of components from a received signal vector is provided comprising performing a QR decomposition of a channel matrix characterizing the communication channel via which the signal vector was received and being expanded by variance information about the noise on the communication channel carrying out a plurality of determination steps using the QR decomposition of the expanded channel matrix, wherein in each step a set of possible sub-vectors of the signal vector is determined and wherein in each step, the number of possible sub-vectors in the set is lower than a predefined maximum number, and selecting one vector of the set of possible sub-vectors determined in the last step of the plurality of determination steps as the signal vector.

Solving Complex-Valued Time-Varying Linear Matrix Equations via QR Decomposition With Applications to Robotic Motion Tracking and on Angle-of-Arrival Localization

Abstract: The problem of solving linear equations is considered as one of the fundamental problems commonly encountered in science and engineering. In this article, the complex-valued time-varying linear matrix equation (CVTV-LME) problem is investigated. Then, by employing a complex-valued, time-varying QR (CVTVQR) decomposition, the zeroing neural network (ZNN) method, equivalent transformations, Kronecker product, and vectorization techniques, we propose and study a CVTVQR decomposition-based linear matrix equation (CVTVQR-LME) model. In addition to the usage of the QR decomposition, the further advantage of the CVTVQR-LME model is reflected in the fact that it can handle a linear system with square or rectangular coefficient matrix in both the matrix and vector cases. Its efficacy in solving the CVTV-LME problems have been tested in a variety of numerical simulations as well as in two applications, one in robotic motion tracking and the other in angle-of-arrival localization.