Quasi-Monte Carlo Methods for some Linear Algebra Problems. Convergence and Complexity

We present quasi-Monte Carlo analogs of Monte Carlo methods for some linear algebra problems: solving systems of linear equations, computing extreme eigenvalues, and matrix inversion. Reformulating the problems as solving integral equations with a special kernels and domains permits us to analyze the quasi-Monte Carlo methods with bounds from numerical integration. Standard Monte Carlo methods for integration provide a convergence rate of O(N^(−1/2)) using N samples. Quasi-Monte Carlo methods use quasirandom sequences with the resulting convergence rate for numerical integration as good as O((logN)^k)N^(−1)). We have shown theoretically and through numerical tests that the use of quasirandom sequences improves both the magnitude of the error and the convergence rate of the considered Monte Carlo methods. We also analyze the complexity of considered quasi-Monte Carlo algorithms and compare them to the complexity of the analogous Monte Carlo and deterministic algorithms.

TQM in e-Learning: a Self-assessment Model and Questionnaire

Organizations are seeking new, integrated systems that enable rapid changes through early identification of opportunities and problems, tracking of progress against plans, flexible allocation of resources to achieve goals, and consistent operations. Total Quality Management (TQM) is an overall business strategy. It means that all activities of the company will be focused on satisfying all stakeholders of the company. TQM can be realised by using the EFQM model. The EFQM model is a tool that organizations may use as a framework for self-evaluation that enables an organization to identify its strengths and areas for improvement and the extent to which its operations and results are in line with the characteristics of an excellent organization. We focus on a training organisation or to the learning department of an organization. So we are limiting the EFQM model to the training /learning activities. We can apply EFQM perfect on the level of an activity (business line) of a company. We selected the main criteria for which the learner can play the role of assessor. So only three main criteria left: the enabling resources, the enabling processes and the (learning) results for the learner. We limited the last one to “learning results” based on the Kirkpatrick model.

Teaching University-Level Mathematics Using Mathematica

This paper considers the use of the computer algebra system Mathematica for teaching university-level mathematics subjects. Outlined are basic Mathematica concepts, connected with different mathematics areas: algebra, linear algebra, geometry, calculus and analysis, complex functions, numerical analysis and scientific computing, probability and statistics. The course “Information technologies in mathematics”, which involves the use of Mathematica, is also presented - discussed are the syllabus, aims, approaches and outcomes.

Stochastic Arithmetic Theory and Experiments

Stochastic arithmetic has been developed as a model for exact computing with imprecise data. Stochastic arithmetic provides confidence intervals for the numerical results and can be implemented in any existing numerical software by redefining types of the variables and overloading the operators on them. Here some properties of stochastic arithmetic are further investigated and applied to the computation of inner products and the solution to linear systems. Several numerical experiments are performed showing the efficiency of the proposed approach.

Automated Assessment of Student Activity in Moodle

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2014