Austrian Academy of Sciences
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Danksagung der Autoren. Sitzungsberichte der philosophisch-historischen Klasse|Migration und Staatsbürgerschaft Migration und ... 1|
The life course and subjective well-being across generations – an analysis based on cross-national surveys (2002–2016). Vienna Yearbook of Population Research|Vienna Yearbook of Population Research 2021|
This paper identifies subjective well-being trajectories through happiness measures as influenced by time, socio-economic, demographic and behavioural determinants. Hierarchical age-period-cohort models are applied to European Social Survey (2002–2016) data on the population aged 30 and older in 10 countries. A U-shaped relationship between age and happiness is found for some countries, but a rather flat pattern and considerable diversity beyond age 80 are detected for other countries. Lower happiness levels are found for baby boomers (1945–1964) than for preboomers and post-boomers, and also for late boomers (1955–1964) than for early boomers (1945–1954). Women, highly educated and native people are shown to have higher happiness levels than men, less educated and non-native people, respectively. Moreover, a positive assessment of income, having a partner, and being a parent, in good health, employed and socially active are all found to have a positive impact on happiness levels. We find evidence of gaps in happiness levels due to differences in socio-economic characteristics over the life course in some, but not in all of the countries analysed
A stable matrix version of the fast multipole method: stabilization strategies and examples. ETNA - Electronic Transactions on Numerical Analysis
The fast multipole method (FMM) is an efficient method for evaluating matrix-vector products related to certain discretized kernel functions. The method involves an underlying FMM matrix given by a sequence of smaller matrices (called generators for convenience). Although there has been extensive work in designing and applying FMM techniques, the stability of the FMM and the stable FMM matrix factorization have rarely been studied. In this work, we propose techniques that lead to stable operations with FMM matrices. One key objective is to give stabilization strategies that can be used to provide low-rank approximations and translation relations in the FMM satisfying some stability requirements. The standard Taylor expansions used in FMMs yield basis generators susceptible to instability. Here, we introduce some scaling factors to control the relevant norms of the generators and give a rigorous analysis of the bounds of the entrywise magnitudes. The second objective is to use the one-dimensional case as an example to provide an intuitive construction of FMM matrices satisfying some stability conditions and then convert an FMM matrix into a hierarchically semiseparable (HSS) form that admits stable ULV-type factorizations. This bridges the gap between the FMM and stable FMM matrix factorizations. The HSS construction is done analytically and does not require expensive algebraic compression. Relevant stability studies are given, which show that the resulting matrix forms are suitable for stable operations. Note that the essential stabilization ideas are also applicable to higher dimensions. Extensive numerical tests are given to illustrate the reliability and accuracy