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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01 Jan 2010
24 citations
TL;DR: The utility, reliability and speed of these algorithms are a consequence of the algorithm for computing the minimal dimension state space transition matrix for models with arbitrary numbers of lags or leads.
24 citations
10 Aug 1998
TL;DR: For performing Givens rotations in the QR decomposition recursive least squares adaptive filter, logarithmic arithmetic is shown to compare favorably to other strength reduction techniques, such as CORDIC arithmetic, in terms of switched capacitance and numerical accuracy.
Abstract: An important technique for reducing pow er consumption in VLSI systems is strength reduction, the substitution of a less-costly operation such as a shift, for a more-costly operation such a multiplication. Using a logarithmic number represen tation provides sev eral opportunities for strength reductions; in particular, m ultiplicationis performed as the fixed-point addition of logarithms, and extracting a square root is implemented via a shift. These reductions occur transparently at the hardware level; consequently relativ ely little algorithmic modification is required, and they are readily applicable to adaptive filtering. For performing Givens rotations in the QR decomposition recursiv e least squares adaptive filter, logarithmic arithmetic is shown to compare favorably to other strength reduction techniques, such as CORDIC arithmetic, in terms of switched capacitance and numerical accuracy.
24 citations
16 Oct 1995
TL;DR: An algorithm for recursive least squares optimisation based on the method of QR decomposition by Givens rotations is reformulated in terms of parameters whose magnitude is never greater than one to enable the design of a much simpler application specific integrated circuit to implement the G Vivens rotation processor for adaptive filtering and beamforming.
Abstract: An algorithm for recursive least squares optimisation based on the method of QR decomposition by Givens rotations is reformulated in terms of parameters whose magnitude is never greater than one. In view of the direct analogy to statistical normalisation, it is referred to as the normalised Givens rotation algorithm. An important consequence of the normalisation is that most of the resulting least squares computation may be carried out using fixed point arithmetic. This should enable the design of a much simpler application specific integrated circuit to implement the Givens rotation processor for adaptive filtering and beamforming.
24 citations
Proceedings Article•
08 Dec 2014TL;DR: L-CCA as mentioned in this paper is an iterative algorithm which can compute Canonical Correlation Analysis (CCA) fast on huge sparse datasets, which is a widely used statistical tool with both established theory and favorable performance for a wide range of machine learning problems.
Abstract: Canonical Correlation Analysis (CCA) is a widely used statistical tool with both well established theory and favorable performance for a wide range of machine learning problems. However, computing CCA for huge datasets can be very slow since it involves implementing QR decomposition or singular value decomposition of huge matrices. In this paper we introduce L-CCA , a iterative algorithm which can compute CCA fast on huge sparse datasets. Theory on both the asymptotic convergence and finite time accuracy of L-CCA are established. The experiments also show that L-CCA outperform other fast CCA approximation schemes on two real datasets.
24 citations