93 research outputs found

    How long does it take to compute the eigenvalues of a random symmetric matrix?

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    We present the results of an empirical study of the performance of the QR algorithm (with and without shifts) and the Toda algorithm on random symmetric matrices. The random matrices are chosen from six ensembles, four of which lie in the Wigner class. For all three algorithms, we observe a form of universality for the deflation time statistics for random matrices within the Wigner class. For these ensembles, the empirical distribution of a normalized deflation time is found to collapse onto a curve that depends only on the algorithm, but not on the matrix size or deflation tolerance provided the matrix size is large enough (see Figure 4, Figure 7 and Figure 10). For the QR algorithm with the Wilkinson shift, the observed universality is even stronger and includes certain non-Wigner ensembles. Our experiments also provide a quantitative statistical picture of the accelerated convergence with shifts.Comment: 20 Figures; Revision includes a treatment of the QR algorithm with shift

    Indoor Air Quality Emissions & Modelling System (IAQ-EMS) - Indoor Air pollutants database

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    The datasets included are the literary review made on all the available research relative to indoor air pollution in the UK, methodologies of conversion of sampled concentrations in emission rates and calculated emission rates from different indoor activities. The dataset has been developed by the University of Birmingham as part of the Clean Air programme "Indoor Air Quality Emissions & Modelling System" (https://www.ukcleanair.org/)
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