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The corresponding normalised singular value spectra are plotted in Additional file 1, Figure S4.
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The purpose of this paper is introduce a new preconditioning process through altering the singular value spectrum of A and then transforming (1.1) into a more benign problem.
The singular value spectrum from the SVD is flatter, with higher-frequency modes appearing more quickly, and in total representing 45% of the total variance present in real stories (see Figures S22 and S25 in Additional file 1).
There Gaudette used the singular value spectrum to quantify how the addition of a second wavelength reduced the ill-posedness of the inverse problem.
According to the NYFR prior information, the chirp singular value ratio spectrum is proposed to estimate the chirp rate.
With filter length increasing, the extremal singular values and spectrum conditions of matrix K are shown in Table 2 to analyze if the corresponding equations represent ill-posed system.
Singular value decomposition, power spectrum enhancement, and the least square fitting techniques are adopted to decouple and obtain the strain modes one by one.
For each participant, the dimensionality of spectra was reduced to 4 frequency modes derived from a singular value decomposition of the spectra (Chen et al. 2009).
Component spectra, identified using singular value decomposition (SVD) analysis, reveal three significant spectral contributions.
CD melt data from 205 30000 nm were deconvoluted into component spectra using the singular value decomposition procedure in Matlab (The Mathworks), and their statistical significance was calculated based on singular values.
The analyses deal with the operators A and A ∗ A, which are based on the singular value decomposition and a more general spectrum, respectively.
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