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    Structured backward errors in linearizations. ETNA - Electronic Transactions on Numerical Analysis

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    A standard approach to calculate the roots of a univariate polynomial is to compute the eigenvalues of an associated confederate matrix instead, such as, for instance, the companion or comrade matrix. The eigenvalues of the confederate matrix can be computed by Francis's QR algorithm. Unfortunately, even though the QR algorithm is provably backward stable, mapping the errors back to the original polynomial coefficients can still lead to huge errors. However, the latter statement assumes the use of a non-structure-exploiting QR algorithm. In [J. L. Aurentz et al., Fast and backward stable computation of roots of polynomials, SIAM J. Matrix Anal. Appl., 36 (2015), pp. 942–973] it was shown that a structure-exploiting QR algorithm for companion matrices leads to a structured backward error in the companion matrix. The proof relied on decomposing the error into two parts: a part related to the recurrence coefficients of the basis (a monomial basis in that case) and a part linked to the coefficients of the original polynomial. In this article we prove that the analysis can be extended to other classes of comrade matrices. We first provide an alternative backward stability proof in the monomial basis using structured QR algorithms; our new point of view shows more explicitly how a structured, decoupled error in the confederate matrix gets mapped to the associated polynomial coefficients. This insight reveals which properties have to be preserved by a structure-exploiting QR algorithm to end up with a backward stable algorithm. We will show that the previously formulated companion analysis fits into this framework, and we analyze in more detail Jacobi polynomials (comrade matrices) and Chebyshev polynomials (colleague matrices)

    Mortality evolution in Algeria: What can we learn about data quality?. Vienna Yearbook of Population Research|Vienna Yearbook of Population Research 2021|

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    Mortality in Algeria has declined significantly since the country declared its independence in 1962. This trend has been accompanied by improvements in data quality and changes in estimation methodology, both of which are scarcely documented, and may distort the natural evolution of mortality as reported in official statistics. In this paper, our aim is to detect these methodological and data quality changes by means of the visual inspection of mortality surfaces, which represent the evolution of mortality rates, mortality improvement rates and the male-female mortality ratio over age and time. Data quality problems are clearly visible during the 1977–1982 period. The quality of mortality data has improved after 1983, and even further since the population census of 1998, which coincided with the end of the civil war. Additional inexplicable patterns have also been detected, such as a changing mortality age pattern during the period before 1983, and a changing pattern of excess female mortality at reproductive ages, which suddenly appears in 1983 and disappears in 1992

    Multi-Feature Sample Database for Enhancing Deep Learning Tasks in Operational Humanitarian Applications. GI_Forum|GI_Forum 2021, Volume 1|

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    Amongst the many benefits of remote sensing techniques in disaster- or conflict-related applications, timeliness and objectivity may be the most critical assets. Recently, increasing sensor quality and data availability have shifted the attention more towards the information extraction process itself. With promising results obtained by deep learning (DL), the notion arises that DL is not agnostic to input errors or biases introduced, in particular in sample-scarce situations. The present work seeks to understand the influence of different sample quality aspects propagating through network layers in automated image analysis. In this paper, we broadly discuss the conceptualisation of such a sample database in an early stage of realisation: (1) inherited properties (quality parameters of the underlying image such as cloud cover, seasonality, etc.); (2) individual (i.e., per-sample) properties, including a. lineage and provenance, b. geometric properties (size, orientation, shape), c. spectral features (standardized colour code); (3) context-related properties (arrangement Several hundred samples collected from different camp settings were hand-selected and annotated with computed features in an initial stage. The supervised annotation routine is automated so that thousands of existing samples can be labelled with this extended feature set. This should better condition the subsequent DL tasks in a hybrid AI approach

    GW-Unterricht 162. GW-Unterricht|GW-Unterricht 162|

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    Inhalt. GW-Unterricht|GW-Unterricht 163|

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    Rucker, Charlotte (eig. Carolina, verw. Tschörner, gesch. Boyes)

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    * 2.11.1852 Schwaz in Tirol, † 23.4.1904 Wien. Pianistin, Pädagogin

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