A block toeplitz look-ahead schur algorithm

Gallivan, Kyle A.; Thirumalai, S.; Dooren, Paul Van

doi:10.1016/b978-044482107-2/50019-4

Cited by 4 publications

(2 citation statements)

References 10 publications

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“…A rst idea to overcome instable behavior of the classical algorithms is to \look ahead" from one well-conditioned section to the next one and jump over the illconditioned sections that lie in between. For Toeplitz systems several look-ahead algorithms were designed in 10,11,14,15,17,22,24,25,26,27,34]. For Hankel systems we refer to 6,9,16].…”

Section: Introduction Subject Of the Paper Are Linear Systems Of Equmentioning

confidence: 99%

A Stabilized Superfast Solver for Nonsymmetric Toeplitz Systems

Barel

Heinig²,

Kravanja³

2001

SIAM J. Matrix Anal. & Appl.

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We present a stabilized superfast solver for nonsymmetric Toeplitz systems Tx = b. An explicit formula for T 1 is expressed in such a way that the matrixvector product T 1 b can be calculated via FFTs and Hadamard products. This inversion formula involves certain polynomials that can be computed by solving two linearized rational interpolation problems on the unit circle. The heart of our Toeplitz solver is a superfast algorithm to solve these interpolation problems. This algorithm is stabilized via pivoting, iterative improvement, downdating, and by giving \di cult" interpolation points an adequate treatment. We have implemented our algorithm in Fortran 90. Numerical examples illustrate the e ectiveness of our approach.

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Section: Introduction Subject Of the Paper Are Linear Systems Of Equmentioning

confidence: 99%

A Stabilized Superfast Solver for Nonsymmetric Toeplitz Systems

Barel

Heinig²,

Kravanja³

2001

SIAM J. Matrix Anal. & Appl.

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“…Then, since R is a symmetric block-toeplitz matrix, the optimal solution g opt in (3.1) can be computed with the Levinson-Durbin solver with O (LI g ) 2 operations by recursively iterating from order 0 to order I g −1. Alternatively, the optimal solution can be obtained with a fast solver based on the Schur algorithm [89,90], which exploits the block-toeplitz structure of R to compute its Cholesky factorization with O (LI g ) 2 operations [91].…”

Section: Fast Solversmentioning

confidence: 99%

Filter Optimization for Personal Sound Zones Systems

Cases¹

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Personal Sound Zones (PSZ) systems deliver different sounds to a number of listeners sharing an acoustic space through the use of loudspeakers together with signal processing techniques. These systems have attracted a lot of attention in recent years because of the wide range of applications that would benefit from the generation of individual listening zones, e.g., domestic or automotive audio applications. A key aspect of PSZ systems, at least for low and mid frequencies, is the optimization of the filters used to process the sound signals. Different algorithms have been proposed in the literature for computing those filters, each exhibiting some advantages and disadvantages. In this work, the state-of-the-art algorithms for PSZ systems are reviewed, and their performance in a reverberant environment is evaluated. Aspects such as the acoustic isolation between zones, the reproduction error, the energy of the filters, and the delay of the system are considered in the evaluations. Furthermore, computationally efficient strategies to obtain the filters are studied, and their computational complexity is compared too. The performance and computational evaluations reveal the main limitations of the state-of-the-art algorithms. In particular, the existing solutions can not offer low computational complexity and at the same time good performance for short system delays. Thus, a novel algorithm based on subband filtering that mitigates these limitations is proposed for PSZ systems. In addition, the proposed algorithm offers more versatility than the existing algorithms, since different system configurations, such as different filter lengths or sets of loudspeakers, can be used in each subband. The proposed algorithm is experimentally evaluated and tested in a reverberant environment, and its efficacy to mitigate the limitations of the existing solutions is demonstrated. Finally, the effect of the target responses in the optimization is discussed, and a novel approach that is based on windowing the target responses is proposed. The proposed approach is experimentally evaluated in two rooms with different reverberation levels. The evaluation results reveal that an appropriate windowing of the target responses can reduce the interference level between zones.

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Subspace techniques in blind mobile radio channel identification and equalization using fractional spacing and/or multiple antennas

Slock

1995

SVD and Signal Processing III

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A block toeplitz look-ahead schur algorithm

Cited by 4 publications

References 10 publications

A Stabilized Superfast Solver for Nonsymmetric Toeplitz Systems

A Stabilized Superfast Solver for Nonsymmetric Toeplitz Systems

Filter Optimization for Personal Sound Zones Systems

Subspace techniques in blind mobile radio channel identification and equalization using fractional spacing and/or multiple antennas

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