Jurjen Duintjer Tebbens

Efficient Preconditioning of Sequences of Nonsymmetric Linear Systems

We present a new approach for approximate updates of factorized nonsymmetric preconditioners for solving sequences of linear algebraic systems. This approach is algebraic and it is theoretically motivated. It generalizes diagonal updates introduced by Benzi and Bertaccini [BIT, 43 (2003), pp. 231-244] and Bertaccini [Electron. Trans. Numer. Anal., 18 (2004), pp. 49-64]. It is shown experimentally that this approach can be very beneficial. For example, it is successful in significantly decreasing the number of iterations of a preconditioned iterative method for solving subsequent systems of a sequence when compared with freezing the preconditioner from the first system of the sequence. In some cases, the updated preconditioners offer a rate of convergence similar to or even higher than the rate obtained when preconditioning with recomputed preconditioners. Since the updates are typically cheap and straightforward, their use is of practical interest. They can replace recomputing preconditioners, which is often expensive, especially in parallel and matrix-free environments.

Improving implementation of linear discriminant analysis for the high dimension/small sample size problem

Classification based on Fishers linear discriminant analysis (FLDA) is challenging when the number of variables largely exceeds the number of given samples. The original FLDA needs to be carefully modified and with high dimensionality implementation issues like reduction of storage costs are of crucial importance. Methods are reviewed for the high dimension/small sample size problem and the one closest, in some sense, to the classical regular approach is chosen. The implementation of this method with regard to computational and storage costs and numerical stability is improved. This is achieved through combining a variety of known and new implementation strategies. Experiments demonstrate the superiority, with respect to both overall costs and classification rates, of the resulting algorithm compared with other methods.

Preconditioner updates for solving sequences of linear systems in matrix-free environment

SUMMARY We present two new ways of preconditioning sequences of nonsymmetric linear systems in the special case where the implementation is matrix free. Both approaches are fully algebraic, they are based on the general updates of incomplete LU decompositions recently introduced in (SIAM J. Sci. Comput. 2007; 29(5):1918–1941), and they may be directly embedded into nonlinear algebraic solvers. The first of the approaches uses a new model of partial matrix estimation to compute the updates. The second approach exploits separability of function components to apply the updated factorized preconditioner via function evaluations with the discretized operator. Experiments with matrix-free implementations of test problems show that both new techniques offer useful, robust and black-box solution strategies. In addition, they show that the new techniques are often more efficient in matrix-free environment than either recomputing the preconditioner from scratch for every linear system of the sequence or than freezing the preconditioner throughout the whole sequence. Copyright q 2010 John Wiley & Sons, Ltd. Received 11 December 2008; Revised 16 November 2009; Accepted 4 December 2009

Any Ritz Value Behavior Is Possible for Arnoldi and for GMRES

We show that arbitrary convergence behavior of Ritz values is possible in the Arnoldi method, and we give two parametrizations of the class of matrices with initial Arnoldi vectors that generate prescribed Ritz values (in all iterations). The second parametrization enables us to prove that any GMRES residual norm history is possible with any prescribed Ritz values (in all iterations), provided that we treat the stagnation case appropriately.

Delay in the diagnosis and treatment of pulmonary tuberculosis in Uzbekistan: a cross-sectional study

BackgroundEarly diagnosis and prompt effective therapy are crucial for the prevention of tuberculosis (TB) transmission, particularly in regions with high levels of multi-drug resistant TB. This study aimed to evaluate the extent of delay in diagnosis and treatment of TB in Uzbekistan and identify associated risk factors.MethodsA cross-sectional study was performed on hospital patients with newly diagnosed TB. The time between the onset of respiratory symptoms and initiation of anti-TB treatment was assessed and delays were divided into patient, health system and total delays. Univariable and multivariable logistic regression analysis was used to evaluate determinants of diagnostic and treatment delay.ResultsAmong 538 patients enrolled, the median delay from onset of symptoms until treatment with anti-TB drugs was 50 days. Analysis of the factors affecting health-seeking behaviour and timely treatment showed the presence of the patient factor. Self-medication was the first health-seeking action for 231 (43%) patients and proved to be a significant predictor of delay (p = 0.005), as well as coughing (p = 0.009), loss of weight (p = 0.001), and visiting private and primary healthcare facilities (p = 0.03 and p = 0.02, respectively).ConclusionTB diagnostic and treatment delay was mainly contributed to by patient delay and should be reduced through increasing public awareness of TB symptoms and improving public health-seeking behaviour for timely initiation of anti-TB treatment. Efforts should be made to minimise irrational use of antibiotics and support interventions to restrict over-the-counter availability of antibiotics.

The role eigenvalues play in forming GMRES residual norms with non-normal matrices

In this paper we give explicit expressions for the norms of the residual vectors generated by the GMRES algorithm applied to a non-normal matrix. They involve the right-hand side of the linear system, the eigenvalues, the eigenvectors and, in the non-diagonalizable case, the principal vectors. They give a complete description of how eigenvalues contribute in forming residual norms and offer insight in what quantities can prevent GMRES from being governed by eigenvalues.

Prescribing the behavior of early terminating GMRES and Arnoldi iterations

We generalize and extend results of the series of papers by Greenbaum and Strakoš (IMA Vol Math Appl 60:95–118, 1994), Greenbaum et al. (SIAM J Matrix Anal Appl 17(3):465–469, 1996), Arioli et al. (BIT 38(4):636–643, 1998) and Duintjer Tebbens and Meurant (SIAM J Matrix Anal Appl 33(3):958–978, 2012). They show how to construct matrices with right-hand sides generating a prescribed GMRES residual norm convergence curve as well as prescribed Ritz values in all iterations, including the eigenvalues, and give parametrizations of the entire class of matrices and right-hand sides with these properties. These results assumed that the underlying Arnoldi orthogonalization processes are breakdown-free and hence considered non-derogatory matrices only. We extend the results with parametrizations of classes of general nonsingular matrices with right-hand sides allowing the early termination case and also give analogues for the early termination case of other results related to the theory developed in the papers mentioned above.

Antibiotic use practices of pharmacy staff: a cross-sectional study in Saint Petersburg, the Russian Federation

BackgroundNon-prescription access to antimicrobials is common, and self-prescribing is increasingly popular in Russian society. The aim of this study was to assess the attitudes of community pharmacists regarding antibiotic use and self-medication.MethodsWe conducted a cross-sectional study from September-December 2015 of community pharmacists in the Saint-Petersburg and Leningrad region, Russia. A self-administered questionnaire was used to assess antibiotic use and self-medication practices. The data were analysed using logistic regression and Pearson chi-squared tests.ResultsOf the 316 pharmacists (77.07%) who completed the questionnaire, 230 (72.8%) self-medicated with antibiotics. Antibiotics were mostly used to self-treat upper (53.3%) and lower respiratory tract infections (19.3%), relying on their own knowledge (81.5%), previous treatment experience (49%) and patients’ prescriptions (17%). The most commonly used antibiotics were macrolides (33.2%). Characteristics such as age, education and experience were related to antibiotic use and self-medication.ConclusionsThe study confirmed that self-prescription of antibiotics is a common practice amongst pharmacists in Saint Petersburg and also identified personal and professional characteristics of pharmacists strongly associated with self-medication.

Knowledge, awareness, and attitudes toward antibiotic use and antimicrobial resistance among Saudi population

Background Inappropriate use of antibiotics is a public health problem of great concern. Objective To evaluate knowledge of antibiotics, race, gender and age as independent risk factors for self-medication. Setting Residents and population from different regions of Saudi Arabia. Methods We conducted a cross sectional survey study among residents. Data were collected between June 2014 to May, 2015 from 1310 participants and data were recorded anonymously. The questionnaire was randomly distributed by interview of participants and included sociodemographic characteristics, antibiotics knowledge, attitudes and behavior with respect to antibiotics usage. Main outcome measure Population aggregate scores on questions and data were analyzed using univariate logistic regression to evaluate the influence of variables on self-prescription of antibiotics. Results The response rate was 87.7xa0%. A cumulative 63.6xa0% of participants reported to have purchased antibiotics without a prescription from pharmacies; 71.1xa0% reported that they did not finish the antibiotic course as they felt better. The availability of antibiotics without prescription was found to be positively associated with self-medication (OR 0.238, 95xa0% CI 0.17–0.33). Of those who used prescribed or non-prescribed antibiotics, 44.7xa0% reported that they kept left-over antibiotics from the incomplete course of treatment for future need. Interestingly, 62xa0% of respondents who used drugs without prescription agreed with the statement that antibiotics should be access-controlled prescribed by a physician. We also found significant association between storage, knowledge/attitudes and education. Conclusions The overall level of awareness on antibiotics use among residents in Saudi Arabia is low. This mandates public health awareness intervention programs to be implemented on the use of antibiotics.

Algorithms for Regularized Linear Discriminant Analysis

This paper is focused on regularized versions of classification analysis and their computation for highdimensional data. A variety of regularized classification methods has been proposed and we critically discuss their computational aspects. We formulate several new algorithms for regularized linear discriminant analysis, which exploits a regularized covariance matrix estimator towards a regular target matrix. Numerical linear algebra considerations are used to propose tailor-made algorithms for specific choices of the target matrix. Further, we arrive at proposing a new classification method based on L2-regularization of group means and the pooled covariance matrix and accompany it by an efficient algorithm for its computation.