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For symmetric (hermitian) (dense or banded) matrices the computation of eigenvalues and eigenvectors Ax = λBx is an important task, e.g. in electronic structure calculations. If a larger number of eigenvectors are needed, often direct solvers are applied. On parallel architectures the ELPA implementation has proven to be very efficient, also compared to other parallel solvers like EigenExa or MAGMA. The main improvement that allows better parallel efficiency in ELPA is the two-step transformation of dense to band to tridiagonal form. This was the achievement of the ELPA project. The continuation of this project has been targeting at additional improvements like allowing monitoring and autotuning of the ELPA code, optimizing the code for different architectures, developing curtailed algorithms for banded A and B, and applying the improved code to solve typical examples in electronic structure calculations. In this paper we will present the outcome of this project.

Introduction and Aims\ud The International Alcohol Control (IAC) Study is a multi‐country collaborative project to assess patterns of alcohol consumption and the impact of alcohol control policy. The aim of this paper is to report the methods and implementation of the IAC.\ud \ud Design and Methods\ud The IAC has been implemented among drinkers 16–65 years in high‐ and middle‐income countries: Australia, England, Scotland, New Zealand, St Kitts and Nevis, Thailand, South Africa, Peru, Mongolia and Vietnam (the latter four samples were sub‐national). Two research instruments were used: the IAC survey of drinkers and the Alcohol Environmental Protocol (a protocol for policy analysis). The survey was administered via computer‐assisted interview and the Alcohol Environmental Protocol data were collected via document review, administrative or commercial data and key informant interviews.\ud \ud Results\ud The IAC instruments were readily adapted for cross‐country use. The IAC methodology has provided cross‐country survey data on key measures of alcohol consumption (quantity, frequency and volume), aspects of policy relevant behaviour and policy implementation: availability, price, purchasing, marketing and drink driving. The median response rate for all countries was 60% (range 16% to 99%). Where data on alcohol available for consumption were available the validity of survey consumption measures were assessed by calculating survey coverage found to be 86% or above. Differential response bias was handled, to the extent it could be, using post‐stratification weights.\ud \ud Discussion and Conclusions\ud The IAC study will allow for cross‐country analysis of drinking patterns, the relationship between alcohol use and policy relevant behaviour in different countries.

Introduction and Aims: \ud \ud Cross‐country studies on alcohol purchasing and access are rare. We examined where and when people access alcohol to understand patterns of availability across a range of middle‐ and high‐income countries.\ud \ud Design and Methods: \ud \ud Surveys of drinkers in the International Alcohol Control study in high‐income countries (Australia, England, Scotland, New Zealand and St Kitts and Nevis) and middle‐income countries (Mongolia, South Africa, Peru, Thailand and Vietnam) were analysed. Measures were: location of purchase from on‐premise and take‐away outlets, proportion of alcohol consumed on‐premise versus take‐away outlets, hours of purchase, access among underage drinkers and time to access alcohol.\ud \ud Results: \ud \ud On‐premise purchasing was prevalent in the high‐income countries. However, the vast majority of alcohol consumed in all countries, except St Kitts and Nevis (high‐income), was take‐away. Percentages of drinkers purchasing from different types of on‐premise and take‐away outlets varied between countries. Late purchasing was common in Peru and less common in Thailand and Vietnam. Alcohol was easily accessed by drinkers in all countries, including underage drinkers in the middle‐income countries.\ud \ud Discussion and Conclusions: \ud \ud In nine out of 10 countries the vast majority of alcohol consumed was take‐away. Alcohol was readily available and relatively easy for underage drinkers to access, particularly in the middle‐income countries. Research is needed to assess the harms associated with take‐away consumption including late at night. Attention is needed to address the easy access by underage drinkers in the middle‐income countries which has been less of a focus than in high‐income countries.

INTRODUCTION AND AIMS: To investigate if socio-economic disadvantage, at the individual- and country-level, is associated with heavier drinking in some middle- and high-income countries. DESIGN AND METHODS: Surveys of drinkers were undertaken in some high- and middle-income countries. Participating countries were Australia, England, New Zealand, Scotland (high-income) and Peru, Thailand and Vietnam (middle-income). Disadvantage at the country-level was defined as per World Bank (categorised as middle-or high-income); individual-level measures were (i) years of education and (ii) whether and individual was under or over the poverty line in each country. Measures of heavier drinking were (i) proportion of drinkers that consumed 8+ drinks and (ii) three drinking risk groups (lower, increasing and higher). Multi-level logistic regression models were used. RESULTS: Individual-level measures of disadvantage, lower education and living in poverty, were associated with heavier drinking, consuming 8+ drinks on a typical occasion or drinking at the higher risk level, when all countries were considered together. Drinkers in the middle-income countries had a higher probability of consuming 8+ drinks on a typical occasion relative to drinkers in the high-income countries. Interactions between country-level income and individual-level disadvantage were undertaken: disadvantaged drinkers in the middle-income countries were less likely to be heavier drinkers relative to those with less disadvantage in the high-income countries. DISCUSSION AND CONCLUSIONS: Associations between socio-economic disadvantage and heavier drinking vary depending on country-level income. These findings highlight the value of exploring cross-country differences in heavier drinking and disadvantage and the importance of including country-level measurements to better elucidate relationships.

Introduction and Aims\ud \ud Gender and age patterns of drinking are important in guiding country responses to harmful use of alcohol. This study undertook cross‐country analysis of drinking across gender, age groups in some high‐and middle‐income countries.\ud \ud \ud Design and Methods\ud \ud Surveys of drinkers were conducted in Australia, England, Scotland, New Zealand, St Kitts and Nevis (high‐income), Thailand, South Africa, Mongolia and Vietnam (middle‐income) as part of the International Alcohol Control Study. Drinking pattern measures were high‐frequency, heavier‐typical quantity and higher‐risk drinking. Differences in the drinking patterns across age and gender groups were calculated. Logistic regression models were applied including a measure of country‐level income.\ud \ud \ud Results\ud \ud Percentages of high‐frequency, heavier‐typical quantity and higher‐risk drinking were greater among men than in women in all countries. Older age was associated with drinking more frequently but smaller typical quantities especially in high‐income countries. Middle‐income countries overall showed less frequent but heavier typical quantities; however, the lower frequencies meant the percentages of higher risk drinkers were lower overall compared with high‐income countries (with the exception of South Africa).\ud \ud \ud Discussion and Conclusions\ud \ud High‐frequency drinking was greater in high‐income countries, particularly in older age groups. Middle‐income countries overall showed less frequent drinking but heavier typical quantities. As alcohol use becomes more normalised as a result of the expansion of commercial alcohol it is likely frequency of drinking will increase with a likelihood of greater numbers drinking at higher risk levels.

Item does not contain fulltext Aims To analyse how adolescent drunkenness and frequency of drinking were associated with adult drinking patterns and alcohol control policies. Design, Setting and Participants Cross-sectional survey data on 13- and 15-year-olds in 37 countries who participated in the Health Behaviour in School-Aged Children (HBSC) Study in 2010 (n=144788) were linked to national-level indicators on alcohol control policies and adult drinking patterns. Measurements Outcome measures were self-reported weekly drinking and life-time drunkenness (drunk once or more). Data were analysed using multi-level logistic regression models. Findings In the mutually adjusted models, adolescent drunkenness was associated significantly with high adult alcohol consumption [odds ratio (OR)=3.15 among boys, 95% confidence interval (CI)=2.13-4.64, OR girls=2.44, CI=1.57-3.80] and risky drinking patterns in the adult population (OR boys=2.02, CI=1.33-3.05, OR girls=1.61, CI=1.18-2.18). The level of abstainers in the adult population was also associated significantly with girls' drunkenness; a 10% increase in the number of abstainers in a country reduced the odds of drunkenness with 21% (OR=0.79, CI=0.68-0.90). Weekly drinking was associated significantly with weak restrictions on availability (OR boys=2.82, CI=1.74-4.54, OR girls=2.00, CI=1.15-3.46) and advertising (OR boys=1.56, CI=1.02-2.40, OR girls=1.79, CI=1.10-2.94). Conclusions Comparing data cross-nationally, high levels of adult alcohol consumption and limited alcohol control policies are associated with high levels of alcohol use among adolescents. 12 p.

In this paper we discuss classical sufficient conditions to be satisfied from the grid transfer operators in order to obtain optimal two-grid and V-cycle multigrid methods utilizing the theory for Toeplitz matrices. We derive relaxed conditions that allow the construction of special grid transfer operators that are computationally less expensive while preserving optimality. This is particularly useful when the generating symbol of the system matrix has a zero of higher order, like in the case of higher order PDEs. These newly derived conditions allow the use of rank deficient grid transfer operators. In this case the use of a pre-relaxation iteration that is lacking the smoothing property is proposed. Combining these pre-relaxations with the new rank deficient grid transfer operators yields a substantial reduction of the convergence rate and of the computational cost at each iteration compared with the classical choice for Toeplitz matrices. The proposed strategy, i.e. a rank deficient grid transfer operator plus a specific pre-relaxation, is applied to linear systems whose system matrix is a Toeplitz matrix where the generating symbol is a high-order polynomial. The necessity of using high-order polynomials as generating symbols for the grid transfer operators usually destroys the Toeplitz structure on the coarser levels. Therefore, we discuss some effective and computational cheap coarsening strategies found in the literature. In particular, we present numerical results showing near-optimal behavior while keeping the Toeplitz structure on the coarser levels. © 2014, Springer Science+Business Media Dordrecht.

We investigate the spectral behavior of preconditioned block Toeplitz matrices with small non-Toeplitz blocks. These matrices have a quite different behavior than scalar or mulitlevel Toeplitz matrices. Based on the connection between Toeplitz and Hankel matrices we derive some negative results on eigenvalue clustering for ill-conditioned block Toeplitz matrices. Furthermore, we identify Block Toeplitz matrices that are easy to solve by the preconditioned conjugate gradient method. We derive some useful inequalities that give information on the location of the spectrum of the preconditioned systems. The described analysis also gives information on preconditioning ill-conditioned Toeplitz Schur complement matrices and Toeplitz normal equations. Electronic Transactions on Numerical Analysis

In this paper we propose and analyze preconditioning strategies for Hermitian indefinite linear systems by using indefinite preconditioners: under very elementary assumptions, we show that the eigenvalues are real. Moreover, in the case of multilevel Toeplitz structures, we prove distributional and localization results. These techniques used in connection with the CG, GMRES, BICGstab, and QMR algorithms allow us to solve in an optimal way the corresponding linear systems. A wide numerical experimentation confirms the efficiency of the proposed procedures.

It is well known that Toeplitz matrices arise in many elds of pure and applied mathematics such as Fourier analysis, numerical treatment of partial di erential equations, industrial control theory, Markov chains, signal and image processing (see e.g. Reference [1]). In some of these applications, large Toeplitz linear systems have to be solved in real time and consequently it is crucial to have fast solvers. In the positive de nite case a lot of optimal iterative solvers are known [1] (in the ill-conditioned case as well) based on band and matrix algebra preconditioners or on multigrid strategies (see e.g. Reference [2]). More di cult problems are encountered in the non-de nite=non-Hermitian setting and in the case of multilevel structures. In this paper, we focus our attention on one of the most challenging cases where the considered Toeplitz linear systems have non-Hermitian coe cient matrix. We emphasize that no specialized solvers have been devised for the non-Hermitian case (except for those essentially based on the normal (preconditioned) equations [3–6]). In addition, concerning multilevel structures, it is worth mentioning the series of negative results [7, 8] concerning matrix algebra preconditioners which could be partially overcome by our proposal which is mainly based