Fast QR Algorithms Based on Backward Prediction Errors: A New Implementation and Its Finite Precision Performance

Apolinario, J.A.; Siqueira, M.G.; Diniz, Paulo S. R.

doi:10.1007/s00034-004-7035-z

Cited by 11 publications

(4 citation statements)

References 6 publications

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“…In the case of one single channel, a unified formulation for Fast QRD-LS algorithms is available in [2]. In this paper, a new algorithm based on the a posteriori backward error updating is developed, using an approach similar to the one used in [3].…”

Section: Introductionmentioning

confidence: 99%

A Lattice Version of the Multichannel Fast QRD Algorithm Based on A Posteriori Backward Errors

Ramos

Apolinario

2004

Telecommunications and Networking - ICT 2004

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Fast QR decomposition (QRD) RLS algorithms based on backward prediction errors are well known for their good numerical behavior and their low complexity when compared to similar algorithms with forward error update. Although the basic matrix expressions are similar, their application to multiple channel input signals generate more complex equations. This paper presents a lattice version of the multichannel fast QRD algorithm based on a posteriori backward errors updating. This new algorithm comprises scalar operations only; its modularity and pipelinability favors its systolic array implementation.

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Section: Introductionmentioning

confidence: 99%

A Lattice Version of the Multichannel Fast QRD Algorithm Based on A Posteriori Backward Errors

Ramos

Apolinario

2004

Telecommunications and Networking - ICT 2004

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“…Unified formulations of Fast QRD-RLS algorithms are available in [4], for the single channel case, and in [5], for the multichannel case. In this paper, a new multiple order Multichannel Fast QRD-RLS algorithm is developed from the fixed order multichannel algorithm recently proposed in [6], using an approach similar to…”

Section: Introductionmentioning

confidence: 99%

A New Multiple Order Multichannel Fast QRD Algorithm and its Application to Non-linear System Identification

Ramos¹,

Apolinario²

2004

Anais Do XXI Simpósio Brasileiro De Telecomunicações

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Multichannel versions of the Fast QRD-RLS algorithms have been mostly addressed in the literature for channels of equal orders. However, in many applications, such as in the case of the Volterra filtering problem, one has to deal with channels of unequal orders. This, along with the fact that the Fast QRD-RLS algorithms based on backward prediction errors are well known for their good numerical behavior and low complexity, has motivated the development of multichannel Fast QRD-RLS algorithms that cope with these cases. This paper presents a new multichannel Fast QRD-RLS algorithm based on a posteriori backward error updating, comprising scalar operations only, that attains both cases of equal and unequal channel orders.

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“…¦ INCE the first QR Decomposition based Fast RLS algorithm introduced by John Cioffi in 1990 [1], many other Fast QRD-based RLS algorithms were developed [2], [3], [4], [5], [6]. It is known that the fast QR algorithms based on backward prediction errors updating are minimal in system theory sense and backward stable [2], [7].…”

Section: Introductionmentioning

confidence: 99%

Infinite Precision Analysis of the Fast QR Algorithm Based on a Posteriori Backward Prediction Errors

Medina¹,

Diniz

2002

Anais Do 2002 International Telecommunications Symposium

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The conventional QR Decomposition (QRD) method requires order ¢ ¤£ -O[¢ ¥£ ]-multiplications per output samples. However a number of fast QRD algorithms have been proposed with O[¢ ] of complexity. Particularly the Fast QRD algorithm based on a posteriori backward prediction errors is well known for its good numerical behavior and low complexity. This algorithm has two distinct versions and, in order to decide which one to choose for a given implementation, its infinite precision analysis of the mean square values of the internal variables would be required. In addition to this implementation issue, the finite-precision analysis requires the estimates of these mean square values. In this work, we first present an overview of the Fast QRD algorithms based on a posteriori backward prediction errors, followed by an infinite precision analysis of the steady state mean square values of the internal variables. Finally, the validity of the analytical results are verified by computer simulations carried out in a system identification setup. In the appendices, the detailed description of each implementation is listed.

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Fast QR Algorithms Based on Backward Prediction Errors: A New Implementation and Its Finite Precision Performance

Cited by 11 publications

References 6 publications

A Lattice Version of the Multichannel Fast QRD Algorithm Based on A Posteriori Backward Errors

A Lattice Version of the Multichannel Fast QRD Algorithm Based on A Posteriori Backward Errors

A New Multiple Order Multichannel Fast QRD Algorithm and its Application to Non-linear System Identification

Infinite Precision Analysis of the Fast QR Algorithm Based on a Posteriori Backward Prediction Errors

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