In the convergence analysis of the GMRES method for a given matrix A, one quantity of interest is the largest possible residual norm that can be attained, at a given iteration step k, over all unit norm initial vectors. This quantity is called the worst-case GMRES residual norm for A and k. We show that the worst case behavior of GMRES for the matrices A and A is the same, and we analyze proper...

These notes describe some of the material of the course “Algorithms Beyond the Worst Case”, which is part of the Mastermath and DIAMANT programs. Last modified: May 25, 2016.

Dimensionality reduction is often needed in many applications due to the high dimensionality of the data involved. In this paper, we first analyze the scatter measures used in the conventional linear discriminant analysis (LDA) model and note that the formulation is based on the average-case view. Based on this analysis, we then propose a new dimensionality reduction method called worst-case li...

PURPOSE To critically evaluate and compare three worst case optimization methods that have been previously employed to generate intensity-modulated proton therapy treatment plans that are robust against systematic errors. The goal of the evaluation is to identify circumstances when the methods behave differently and to describe the mechanism behind the differences when they occur. METHODS The...

a MD, St Mary Mercy Hospital, Livonia, MI 48154, United States of America b MD, Mount Auburn Hospital, Cambridge, MA 02138, United States of America c Medical Student, Fatima Jinnah Medical College, Lahore 45650, Pakistan Correspondence to Muhammad T Shakoor (e-mail: [email protected]) Dengue virus is presently amongst the most important arthropod-borne infections, from both the medical and p...

We investigate the problem of routing traffic through a congested network in an environment of non-cooperative users. We use the worst-case coordination ratio suggested by Koutsoupias and Papadimitriou to measure the performance degradation due to the lack of a centralized traffic regulating authority. We provide a full characterization of the worst-case coordination ratio in the restricted ass...

In immediate or hard real-time systems the correctness of an operation depends not only upon its logical correctness, but also on the time in which it is is computed. In such systems, it is imperative that operations are performed within a given deadline because missing this deadline constitutes the failure of the complete system. Such systems include medical systems, flight control systems and...