Incomplete factorization constraint preconditioners for saddle-point matrices

We consider the application of the conjugate gradient method to the solution of large symmetric, indefinite linear systems. Special emphasis is put on the use of constraint preconditioners and a new factorization that can reduce the number of flops required by the preconditioning step. Results concerning the eigenvalues of the preconditioned matrix and its minimum polynomial are given. Numerical experiments validate these conclusions

TRIDENT 1 third stage motor separation system

The third stage engine separation system has shown through test and analysis that it can effectively and reliably perform its function. The weight of the hardware associated with this system is well within the targeted value

Optimal solvers for PDE-Constrained Optimization

Optimization problems with constraints which require the solution of a partial differential equation arise widely in many areas of the sciences and engineering, in particular in problems of design. The solution of such PDE-constrained optimization problems is usually a major computational task. Here we consider simple problems of this type: distributed control problems in which the 2- and 3-dimensional Poisson problem is the PDE. The large dimensional linear systems which result from discretization and which need to be solved are of saddle-point type. We introduce two optimal preconditioners for these systems which lead to convergence of symmetric Krylov subspace iterative methods in a number of iterations which does not increase with the dimension of the discrete problem. These preconditioners are block structured and involve standard multigrid cycles. The optimality of the preconditioned iterative solver is proved theoretically and verified computationally in several test cases. The theoretical proof indicates that these approaches may have much broader applicability for other partial differential equations

On implicit-factorization constraint preconditioners

Recently Dollar and Wathen [14] proposed a class of incomplete factorizations for saddle-point problems, based upon earlier work by Schilders [40]. In this paper, we generalize this class of preconditioners, and examine the spectral implications of our approach. Numerical tests indicate the efficacy of our preconditioners

Using constraint preconditioners with regularized saddle-point problems

The problem of finding good preconditioners for the numerical solution of a certain important class of indefinite linear systems is considered. These systems are of a 2 by 2 block (KKT) structure in which the (2,2) block (denoted by -C) is assumed to be nonzero. In Constraint preconditioning for indefinite linear systems , SIAM J. Matrix Anal. Appl., 21 (2000), Keller, Gould and Wathen introduced the idea of using constraint preconditioners that have a specific 2 by 2 block structure for the case of C being zero. We shall give results concerning the spectrum and form of the eigenvectors when a preconditioner of the form considered by Keller, Gould and Wathen is used but the system we wish to solve may have C \neq 0 . In particular, the results presented here indicate clustering of eigenvalues and, hence, faster convergence of Krylov subspace iterative methods when the entries of C are small; such situations arise naturally in interior point methods for optimization and we present results for such problems which validate our conclusions.\ud \ud The first author's work was supported by the OUCL Doctorial Training Accoun

A Bramble-Pasciak-like method with applications in optimization

Saddle-point systems arise in many applications areas, in fact in any situation where an extremum principle arises with constraints. The Stokes problem describing slow viscous flow of an incompressible fluid is a classic example coming from partial differential equations and in the area of Optimization such problems are ubiquitous.\ud In this manuscript we show how new approaches for the solution of saddle-point systems arising in Optimization can be derived from the Bramble-Pasciak Conjugate Gradient approach widely used in PDEs and more recent generalizations thereof. In particular we derive a class of new solution methods based on the use of Preconditioned Conjugate Gradients in non-standard inner products and demonstrate how these can be understood through more standard machinery. We show connections to Constraint Preconditioning and give the results of numerical computations on a number of standard Optimization test examples

Cochrane dementia group turns 21—older and (slightly) wiser

This invited editorial describes the achievements of the last 21 years of the Cochrane Dementia and Cognitive Improvement Group (DR Quinn is the coordinating editor of the group)

Participatory Monitoring of Community-Based Rehabilitation and other Disability- Inclusive Development Programmes: the Development of a Manual and Menu

Purpose: This paper describes a three-year research project leading to the development of the CBR Monitoring Manual and Menu (MM&M). The MM&M is a practical toolkit that meets the needs of CBR managers and stakeholders, and is consistent with the philosophy of CBR and community-based disability-inclusive development. It is designed to produce meaningful and locally useful information and data, based on international data standards where possible, to enable aggregation at regional, national and international levels. Methods: Five complementary workstreams of research were carried out from 2011 to 2014: 1) literature review and analysis; 2) participatory action research with CBR stakeholders; 3) analysis and refinement of validity of concepts and structures; 4) consultation and review; and 5) synthesis of results. This article documents the method and key results of each of the five workstreams, and the lessons learned along the way. Results: The MM&M is now freely available on-line at http://sydney.edu.au/health-sciences/cdrp/projects/cbr-monitoring.shtml. Collaboration among members of the development team continues, chiefly via an on-line group to which new members have been welcomed. Conclusion and Implications: At the time of writing, the MM&M is the only international monitoring product, known to the authors, that consciously sets out to reflect both a ‘bottom- up’ and ‘top-down’ perspective of monitoring information and data. To achieve this for a complex programme such as CBR, and to align with its principles, it was essential to use a multi-component and multi-stage strategy for tool development, involving a diverse multidisciplinary team includingcollaboration with CBR stakeholders

Functional dynamics of the folded ankyrin repeats of I kappa B alpha revealed by nuclear magnetic resonance.

Inhibition of nuclear factor kappaB (NF-kappaB) is mainly accomplished by IkappaB alpha, which consists of a signal response sequence at the N-terminus, a six-ankyrin repeat domain (ARD) that binds NF-kappaB, and a C-terminal PEST sequence. Previous studies with the ARD revealed that the fifth and sixth repeats are only partially folded in the absence of NF-kappaB. Here we report NMR studies of a truncated version of IkappaB alpha, containing only the first four ankyrin repeats, IkappaB alpha(67-206). This four-repeat segment is well-structured in the free state, enabling full resonance assignments to be made. H-D exchange, backbone dynamics, and residual dipolar coupling (RDC) experiments reveal regions of flexibility. In addition, regions consistent with the presence of micro- to millisecond motions occur periodically throughout the repeat structure. Comparison of the RDCs with the crystal structure gave only moderate agreement, but an ensemble of structures generated by accelerated molecular dynamics gave much better agreement with the measured RDCs. The regions showing flexibility correspond to those implicated in entropic compensation for the loss of flexibility in ankyrin repeats 5 and 6 upon binding to NF-kappaB. The regions showing micro- to millisecond motions in the free protein are the ends of the beta-hairpins that directly interact with NF-kappaB in the complex

Peran Orangtua terhadap Pendidikan Agama Anak di Desa Sawah Kecamatan Kampar Utara Kabupaten Kampar

The research purpose to determine the role of parents and religious behavior of children with analyze correlation between the role of parents and religious behavior of children. Role is pattern of behavior or action should be taken by parents in educating children religion. This research conducted at the northern Kampar district Sawah subdistrict Kampar. Population of this research is all heads of families residing in the village Sawah field north of Kampar districts and have children aged adolescent age range 13-15 years who attend school or junior high school equivalent listed in the records of population. There are some elements in this research, the first provides religious education which includes about doing prayers, fasting in Ramadan, reciting Al-Quran, gave infak and respect for older people. The second control the implementation of the child worship, control activities carried out by taking action if children do not practice their religion. Third, encourage children to worship that parents set an example and encourage children worship together. Fourth, be patient that parents are expected to be patient in educating religious behavior of children. This research technique is descriptive quantitative, to describe the results of research in the field with numbers, then described by words or narration. Based on the research in the field found that role of parents in Sawah village is considered to be good for 91,48%, the education of children in the Sawah village also rated as good by 95%, there is a strong correlation between the role of parents to religious education of children with result is 0,9 and a significant correlation of 0,01, means there is significant correlation between the role of parents to religious education of children