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.

A one dimensional systolic array for solving arbitrarily large least mean square problems

Abstract: The design is presented of a one-dimensional systolic array for solving arbitrarily large least-mean-square problems involving QR decomposition and a triangular system of equations. The main characteristics of this array are maximization of array utilization, thus achieving a minimum global computation time, and low complexity of the resulting array, which can also be used in problems such as matrix-by-vector, matrix-by-matrix, and LU decomposition. Two systolic algorithms for QR decomposition have been designed. Their chained execution is shown. >

Fine granularity sparse QR factorization for multicore based systems

Abstract: The advent of multicore processors represents a disruptive event in the history of computer science as conventional parallel programming paradigms are proving incapable of fully exploiting their potential for concurrent computations. The need for different or new programming models clearly arises from recent studies which identify fine-granularity and dynamic execution as the keys to achieve high efficiency on multicore systems. This work presents an implementation of the sparse, multifrontal QR factorization capable of achieving high efficiency on multicore systems through using a fine-grained, dataflow parallel programming model.

BD (block diagonalization) pre-coding method and device

Abstract: The invention discloses a BD (block diagonalization) pre-coding method and device, wherein the method comprises the following steps: determining a total user channel matrix Hs according to a downlink channel matrix of each user in a system; carrying out QR factorization on a conjugate transpose matrix of the total user channel matrix Hs to obtain a product of an orthogonal matrix Q and an upper triangular matrix R, and expressing the total user channel matrix Hs as the product of a lower triangular matrix L and a conjugate transpose matrix QH of the orthogonal matrix Q; carrying out inverse calculation on the lower triangular matrix L to obtain L-1; according to the inversed L-1 of the lower triangular matrix L and the orthogonal matrix Q, obtaining a null space orthogonal basis of an interference channel matrix of each user; according to the null space orthogonal basis of the interference channel matrix of each user, constructing a linear pre-coding matrix of each user; and carrying out linear pre-coding on a transmitting signal of each user by utilizing the constructed linear pre-coding matrix. The technical scheme disclosed by the invention can reduce the system complexity and improve the coding efficiency.

Certification of the QR factor R and of lattice basis reducedness

Abstract: Given a lattice basis of n vectors in Zn, we propose an algorithm using 12n3+O(n2) floating point operations for checking whether the basis is LLL-reduced. If the basis is reduced then the algorithm will hopefully answer "yes". If the basis is not reduced, or if the precision used is not sufficient with respect to n, and to the numerical properties of the basis, the algorithm will answer "failed". Hence a positive answer is a rigorous certificate. For implementing the certificate itself, we propose a oating point algorithm for computing (certified) error bounds for the R factor of the QR factorization. This algorithm takes into account all possible approximation and rounding errors. The certificate may be implemented using matrix library routines only. We report experiments that show that for a reduced basis of adequate dimension and quality the certificate succeeds, and establish the effectiveness of the certificate. This effectiveness is applied for certifying the output of fastest existing floating point heuristics of LLL reduction, without slowing down the whole process.

The ORD-based least squares lattice algorithm: Some computer simulations using finite wordlengths

Abstract: The QR-decomposition (QSD)-based least-squares lattice algorithm and its architecture are described. This algorithm can be used to solve least-squares minimization problems that involve time-series data. The results of some computer simulation experiments on an adaptive channel equalizer using the QRD-based lattice algorithm are presented. These simulations were performed using limited-precision floating-point arithmetic. The results show that very little penalty is paid in reducing the computational load. The QRD-based lattice algorithm works essentially as well as the QRD-based triangular systolic array but requires only O(p/sup 2/N) operations per time instant as compared with O(p/sup 2/N/sup 2/) for the array. The results also confirm that a square-root-free form of the algorithm is empirically better than the standard form. >