Numerical Analysis

A work on the use of Cell BE and GPUs as accelerators for numerical kernels, algorithms, and computational science and engineering applications. It covers a range of topics on the increased role of these accelerators in scientific computing.

The Monte Carlo method is a numerical method of solving mathematical problems through random sampling. This work demonstrates how practical problems in science, industry, and trade can be solved using this method. It presents various examples of its application, including queuein...g, quality and reliability estimations and neutron transport.
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Algorithms are usually classified based on their convergence order - linear, quadratic, etc - and their convergence rate, defined as a bound as the number of iterates goes to infinity. The rate is calculated with respect to the number of steps (iterates) an algorithm takes to con...verge, with no thought on how much effort is applied at each iterate. This volume demonstrates that the use of partial information, refined at each new iteration of the algorithm, can increase the efficiency of the algorithm, while guaranteeing convergence to the optimal solution, provided that the rate of refinement is carefully chosen. Based on approximate algorithms for problem solving, the authors present a new theory, which serves as a general framework for the problem, and consider general and particularly Markov Decision processes. A more suitable definition of the convergence rate with respect to the computational effort is derived for the proposed class of approximate iterative algorithms. In addition, an optimal refinement strategy is derived, which maximizes the rate of convergence with respect to the computation effort of this class of algorithms. Hence, a class of algorithms is derived that makes optimal use of the computational resources available. With a given, fixed amount of computation time, the proposed class of algorithms gets closer to the solution than any other algorithm, including the classical (exact) algorithm. Many numerical examples are included for illustration. This volume is intended for mathematicians, engineers and computer scientists, who work on learning processes in numerical analysis and are involved with optimization, optimal control, decision analysis and machine learning.
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The design and analysis of experiments is typically taught as part of a second level course in statistics. Many different types and levels of students will require this information in order to progress with their studies and research. This text is thus offered as an introduction ...to this wide ranging and important subject. It has the advantage of explaining in an accessible way the basic principles behind good experimental thinking, planning and action. The authors have used their experience in teaching related courses to separate out what seem to be the essential basic contents for everyone, and to combine with these some of the most useful additional topics in biological, industrial, medical, and environmental experimentation.
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Providing a combination of theory, algorithms, and simulations, this work applies algorithms and discrete mathematics to practical problems in application areas, such as computational biology, computational chemistry, wireless networks, and computer vision. It is suitable for tho...se within computer science, life science, and engineering.
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