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Only O(n) work per eigenpair is needed by our new algorithm.

We are interested in the iterative formula of the generalized inverse, because it is used by our new algorithm.

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In the third section, the materials used in this paper are given and we present the results produced by our new algorithms and a comprehensive comparison between the new algorithms and five other existing algorithms.

However, and in marked contrast to the analyses shown in Fig.  5d, f, the fixations being identified by our new algorithms are relatively more invariant to variations in data quality.

Figure 2 shows the savings obtained by applying our new algorithm.

In Table 1, we list their results and compare them with the results obtained by running our new algorithm on the same datasets.

Figure  4c and 4d shows a comparison of mean fixation durations as reported by hand-coding and our new algorithms.

Figure  13 shows the results of the comparisons between fixation duration as parsed using the fixation detection algorithms provided by the eyetracker manufacturers and our new algorithms.

Because of its low computational complexity and good convergence property, the block-FFT adaptive filtering algorithm is adopted by our new adaptive detection algorithm of the primary user's signal, which is proposed on basis of the matrix accumulation estimation to overcome further the shortcoming of the above-mentioned algorithms.

In this study, we compared the cost-effectiveness of two algorithms for the diagnosis of patients with AARD suspicion: The first algorithm is based on routine practice in our hospital (the Conventional Algorithm (Fig. 1a)), while the second algorithm includes the detection of anti-DFS70 antibodies as previously proposed by our group (the New Algorithm (Fig. 1b)) [1b].

Here we report several findings showing the power of this approach to large-scale hypothesis-free analysis; while such an analysis was hardly conceivable before, is now within the reach for most researchers by using our new methods, algorithms and software.

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