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Each chapter provides an exploration section with problems that deal with software evaluation, selection, modificationm and the solution of not entirely open-ended problems.
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This book covers an extensive range of topics, including round-off and function evaluation, real zeros of a function, integration, ordinary differential equations, optimization, orthogonal functions, Fourier series, and much more. 1989 edition.
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A practical graduate text on Scientific Computing with a focus on numerical solution of partial differential equations and numerical linear algebra. This book, and its associated freely downloadable MATLAB software, is relevant to engineers, applied mathematicians, numerical anal...ysts, and people working in interdisciplinary Scientific Computing.
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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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Focusing on numerical analysis, this text is part of a series which provides mathematicians and mathematics libraries with surveys of areas undergoing active development, and which reflects the changing distinct areas of pure and applied mathematics.
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This book focuses on broadly defined areas of chemical information science- with special emphasis on chemical informatics- and computer-aided molecular design. The computational and cheminformatics methods discussed, and their application to drug discovery, are essential for sust...aining a viable drug development pipeline.
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Using MATLAB[registered] throughout, this book presents introduction to the theory and application of computational methods for the practical use in everyday computing. It features interval computing in numerical analysis, including coverage of interval arithmetic, interval compu...tation, and interval algorithms.
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By Xu, Yuan
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- RRP: $341.00
- $341.00
- In Stock At Publisher
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Presents a systematic study of the common zeros of polynomials in several variables which are related to higher dimensional quadrature. The author uses a new approach which is based on the recent development of orthogonal polynomials in several variables and differs significantly... from the previous ones based on algebraic ideal theory. Featuring a great deal of new work, new theorems and, in many cases, new proofs, this self-contained work will be of great interest to researchers in numerical analysis, the theory of orthogonal polynomials and related subjects.
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This book describes the mathematical theory of regularizing element transformations as foundation for mesh smoothing. It gives a thorough introduction to GETMe based mesh smoothing and its algorithms providing a framework to focus on efficiently improving minimal element quality,... overal mesh quality, and mesh validity. It addresses the improvement of various types of meshes like planar, surface, volumetric, mixed, isotropic or anisotropic meshes and addresses aspects of combining mesh smoothign with topological mesh modifications.
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This book provides in-depth and wide-ranging analyses of the emergence, and subsequent ubiquity, of algorithms in diverse realms of social life. The plurality of Algorithmic Cultures emphasizes: 1) algorithms' increasing importance in the formation of new epistemic and organizati...onal paradigms; and 2) the multifaceted analyses of algorithms across an increasing number of research fields. The authors in this volume address the complex interrelations between social groups and algorithms in the construction of meaning and social interaction. The contributors highlight the performative dimensions of algorithms by exposing the dynamic processes through which algorithms - themselves the product of a specific approach to the world - frame reality, while at the same time organizing how people think about society. With contributions from leading experts from Media Studies, Social Studies of Science and Technology, Cultural and Media Sociology from Canada, France, Germany, UK and the USA, this volume presents cutting edge empirical and conceptual research that includes case studies on social media platforms, gaming, financial trading and mobile security infrastructures.
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