Decay bounds for the numerical quasiseparable preservation in matrix functions

We adapt the method of direct scaling analysis developed earlier for single-particle Anderson models, to the fermionic multiparticle models with finite or infinite interaction on graphs. Combined with a recent eigenvalue concentration bound for multiparticle systems, the new method leads to a simpler proof of the multiparticle dynamical localization with optimal decay bounds in a natural distance in the multiparticle configuration space, for a large class of strongly mixing random external potentials. Earlier results required the random potential to be IID.

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Very badly approximable matrix functions

Selecta Mathematica ◽

10.1007/s00029-005-0001-1 ◽

2005 ◽

Vol 11 (1) ◽

pp. 127-154 ◽

Cited By ~ 3

Author(s):

V. V. Peller ◽

S. R. Treil

Keyword(s):

Matrix Functions ◽

Badly Approximable

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A New Random Data Description and Its Use in Transferring Road Roughness to Vehicle Response

Journal of Engineering for Industry ◽

10.1115/1.3438380 ◽

1974 ◽

Vol 96 (2) ◽

pp. 676-679 ◽

Cited By ~ 1

Author(s):

J. C. Wambold ◽

W. H. Park ◽

R. G. Vashlishan

Keyword(s):

Spectral Density ◽

Frequency Distribution ◽

Descriptive Analysis ◽

Joint Probability ◽

Amplitude Distribution ◽

Matrix Functions ◽

Initial Portion ◽

Power Spectral ◽

Road Roughness ◽

Cross Spectral Density

The initial portion of the paper discusses the more conventional method of obtaining a vehicle transfer function where phase and magnitude are determined by dividing the cross spectral density of the input/output by the power spectral density (PSD) of the input. The authors needed a more descriptive analysis (over PSD) and developed a new signal description called Amplitude Frequency Distribution (AFD); a discrete joint probability of amplitude and frequency with the advantage of retaining amplitude distribution as well as frequency distribution. A better understanding was obtained, and transfer matrix functions were developed using AFD.

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