Applications of nonlinear approximation for problems in learning theory and applied mathematics

A major pillar of approximation theory in establishing the ability of one class of functions to be represented by another. Establishing such a relationship often leads to efficient numerical approximation methods. In this work, several expressibility theorems are established and several novel numerical approximation techniques are also presented. Not only are these novel methods supported by the presented theory, but also, provided numerical experiments show that these novel methods may be applied to a wide range of applications from image compression to the solutions of high-dimensional PDE

Enhancing Real-time Embedded Image Processing Robustness on Reconfigurable Devices for Critical Applications

Nowadays, image processing is increasingly used in several application fields, such as biomedical, aerospace, or automotive. Within these fields, image processing is used to serve both non-critical and critical tasks. As example, in automotive, cameras are becoming key sensors in increasing car safety, driving assistance and driving comfort. They have been employed for infotainment (non-critical), as well as for some driver assistance tasks (critical), such as Forward Collision Avoidance, Intelligent Speed Control, or Pedestrian Detection. The complexity of these algorithms brings a challenge in real-time image processing systems, requiring high computing capacity, usually not available in processors for embedded systems. Hardware acceleration is therefore crucial, and devices such as Field Programmable Gate Arrays (FPGAs) best fit the growing demand of computational capabilities. These devices can assist embedded processors by significantly speeding-up computationally intensive software algorithms. Moreover, critical applications introduce strict requirements not only from the real-time constraints, but also from the device reliability and algorithm robustness points of view. Technology scaling is highlighting reliability problems related to aging phenomena, and to the increasing sensitivity of digital devices to external radiation events that can cause transient or even permanent faults. These faults can lead to wrong information processed or, in the worst case, to a dangerous system failure. In this context, the reconfigurable nature of FPGA devices can be exploited to increase the system reliability and robustness by leveraging Dynamic Partial Reconfiguration features. The research work presented in this thesis focuses on the development of techniques for implementing efficient and robust real-time embedded image processing hardware accelerators and systems for mission-critical applications. Three main challenges have been faced and will be discussed, along with proposed solutions, throughout the thesis: (i) achieving real-time performances, (ii) enhancing algorithm robustness, and (iii) increasing overall system's dependability. In order to ensure real-time performances, efficient FPGA-based hardware accelerators implementing selected image processing algorithms have been developed. Functionalities offered by the target technology, and algorithm's characteristics have been constantly taken into account while designing such accelerators, in order to efficiently tailor algorithm's operations to available hardware resources. On the other hand, the key idea for increasing image processing algorithms' robustness is to introduce self-adaptivity features at algorithm level, in order to maintain constant, or improve, the quality of results for a wide range of input conditions, that are not always fully predictable at design-time (e.g., noise level variations). This has been accomplished by measuring at run-time some characteristics of the input images, and then tuning the algorithm parameters based on such estimations. Dynamic reconfiguration features of modern reconfigurable FPGA have been extensively exploited in order to integrate run-time adaptivity into the designed hardware accelerators. Tools and methodologies have been also developed in order to increase the overall system dependability during reconfiguration processes, thus providing safe run-time adaptation mechanisms. In addition, taking into account the target technology and the environments in which the developed hardware accelerators and systems may be employed, dependability issues have been analyzed, leading to the development of a platform for quickly assessing the reliability and characterizing the behavior of hardware accelerators implemented on reconfigurable FPGAs when they are affected by such faults

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal