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.
Papers published on a yearly basis
Papers
More filters
04 Apr 1986
TL;DR: A unified checksum scheme for the LU decomposition, Gaussian elimination with pairwise pivoting and the QR decomposition is introduced and how to represent the error as a rank-one perturbation to the original data is shown.
Abstract: We introduce a unified checksum scheme for the LU decomposition, Gaussian elimination with pairwise pivoting and the QR decomposition. The purpose is to detect and locate a transient error during a systolic array computation. We show how to represent the error as a rank-one perturbation to the original data, so that we need not worry when the error occurred. Finally, we perform a floating point error analysis to determine the effects of rounding errors on the check-sum scheme.
18 citations
TL;DR: A parallel algorithm for the calculation of the QR factorization on a hypercube architecture of the SIMD type with distributed memory is described, choosing the modified Gram-Schmidt method with pivoting as it is characterized by good numerical stability.
18 citations
TL;DR: Three reduced complexity equalization schemes for Zero-padded OFDM systems are described and it is shown that the attractive scheme depends on the system specifications.
Abstract: Three reduced complexity equalization schemes for Zero-padded OFDM systems are described. These schemes guarantee Zero-Forcing (ZF) equalization irrespective of the channel nulls. Two of these schemes implement the minimum-norm ZF equalizer efficiently using QR decomposition. In the third scheme, the channel zeros are grouped as being inside or outside or on the unit circle. These groups are then equalized sequentially in a manner so as to tackle excess noise amplification. The three schemes are compared for their computational complexity and Bit Error Rate (BER) performance. It is shown that the attractive scheme depends on the system specifications. The BERComputations trade off occurring in the choice of the right algorithm is also highlighted.
18 citations
10 May 1992
TL;DR: The authors present an approach to the development of fast and numerically stable recursive least squares (RLS) algorithms for adaptive nonlinear filtering using QR-decomposition of the data matrix and introduces a pair of QR-RLS adaptive algorithms for second-order Volterra filtering.
Abstract: The authors present an approach to the development of fast and numerically stable recursive least squares (RLS) algorithms for adaptive nonlinear filtering using QR-decomposition of the data matrix. They introduce a pair of QR-RLS adaptive algorithms for second-order Volterra filtering. Both the algorithms are based solely on Given's rotation. Hence both are numerically stable and highly amenable to parallel implementations using arrays. One of the algorithms is a block processing algorithm in the sense that it processes all the channels simultaneously. The other processes the channels sequentially. The sequential algorithm is computationally much more efficient than the block algorithm and is comparable to that of fast RLS Volterra filters. Another attractive feature of sequential processing is that knowledge of the single-channel algorithm can be applied to the multichannel case. >
18 citations
TL;DR: A detailed mathematical justification for the constrained variant of the POD is provided, including a graphical interpretation of the proposed approach, which is applied to the problem of representing the pressure field around a 2D wing, and is compared with the traditional POD.
18 citations