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

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

Backare

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The Impact of Self-Efficacy on Retention in Technical Colleges

Vocational and career training institutes focus their energy and resources on student support services, increasing student retention as it relates to minority populations. Despite these efforts, a specific vocational and career institute in the southeast United States reports a 50% retention rate of students who are enrolled. This case study explored students\u27 descriptions of how self-efficacy supported their perseverance while attending the vocational and career training institute. The conceptual framework included Bandura\u27s notions of self-efficacy and Tinto\u27s integration model. Purposeful sampling strategies were used to interview 10 successfully-retained students enrolled in their 4th term or beyond at the vocational and career institute under study. Data analysis included initial and axial coding, leading to category creation and the identification of key themes. The following themes emerged regarding self-efficacy in the form of support and perseverance: clear personal educational expectations, strong social relations, and various external supports. Further, perceived challenges to self-efficacy and perseverance included family problems, sickness, finances, incarceration, homelessness, and deployment, age, and instructor or student issues at the college site. Recommendations included the development and implementation of tailored and focused student support structures to improve student self-efficacy and perseverance at the local site. Implications for positive social change include providing research findings to the local administration, which may increase their understanding of retention issues and ultimately improve student retention

The Water holes at Ijara

Volume: XXI

Mechanism of thermal decomposition of poly(ether ether ketone) (PEEK) from a review of decomposition studies

A review of the literature on the flammability and decomposition of poly(oxy-1,4-phenyleneoxy-1,4-phenylenecarbonyl-1,4-phenylene) (PEEK) is presented. This paper provides an overview of the flammability of PEEK and its decomposition mechanisms. Based on this literature, mechanisms have been suggested which attempt to explain the products formed at each stage of PEEK decomposition and indicate the intermediates which should be formed at each of these stages

Lantern Of Love

Contains advertisements and/or short musical examples of pieces being sold by publisher.https://digitalcommons.library.umaine.edu/mmb-vp/6939/thumbnail.jp

In Old Ireland, where the River Kenmare Flows

https://digitalcommons.library.umaine.edu/mmb-vp/1850/thumbnail.jp

Baby : Fox-Trot Lullaby

https://digitalcommons.library.umaine.edu/mmb-vp/5471/thumbnail.jp