Austrian Academy of Sciences
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5 Wohnbevölkerung und Wahlberechtigte: Die Entkoppelung von Staatsbürgerschaft, Wohnsitz und Wahlrecht. Sitzungsberichte der philosophisch-historischen Klasse|Migration und Staatsbürgerschaft Migration und ... 1|
No full textIndex. Denkschriften der philosophisch-historischen Klasse|Tribes in Modern Yemen: An Anthology Sammlung Eduard Glaser 18|
No full textCSEL_41 Band_Kern.pdf. Corpus Scriptorum Ecclesiasticorum Latinorum |Corpus Scriptorum Ecclesiasticorum Latinorum Vol. XXXXI Sancti Avreli Augustini XXXXI|
No full textAnhang. Denkschriften der philosophisch-historischen Klasse|Die mittelalterlichen Handschriften in der Bibliothek des Augustiner Chorherrenstiftes Neustift Denkschriften der philosophisch-historischen Klasse 364. Band|
No full textEin Prähistoriker und Unterrichtsminister in der NS-Zeit: Oswald Menghin und die „Kulturkreislehre“ von Pater Wilhelm Schmidt. Veröffentlichungen zur Sozialanthropologie|Völkerkunde zur NS-Zeit aus Wien (1938–1945) Veröffentlichungen zur Sozialanthropologie Band 27/1,2,3|Band 1 Veröffentlichungen zur Sozialanthropologie|
No full textList of Contributors. Archiv für Österreichische Geschichte|The Habsburg Mediterranean 1500–1800|
No full text
Nationalization of Indicators for Sustainable Development Goals in the Republic of Kazakhstan through Geoinformation Technologies. GI_Forum|GI_Forum 2021, Volume 1|
No full textFrom the first days of independence, Kazakhstan has paid attention to sustainable development and successfully achieved the Millennium Development Goals and in 2015 launched the implementation of the 2030 Agenda for Sustainable Development. The article discusses the issues of monitoring and reporting on the SDGs in Kazakhstan, the priority of nationalization of indicators, the creation of a statistical database on the SDGs, the definition of data sources, and methodology for calculation. Geospatial data are inevitable for the integration of information about society, economy and environment. A web-portal developed by the authors is presented that allows to assess the quality of life of the population in different regions based on the SDG indicators
Structured backward errors in linearizations. ETNA - Electronic Transactions on Numerical Analysis
No full textA 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)
