Generating Functions in Engineering and the Applied Sciences, Rajan Chattamvelli , Ramalingam Shanmugam

Автор: Todinov, Michael
Название: Interpretation of algebraic inequalities
ISBN: 1032059176 ISBN-13(EAN): 9781032059174
Издательство: Taylor&Francis
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Цена: 11482.00 р.
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Описание: This book demonstrates how interpreting abstract inequalities can optimise engineering design processes, with applications in mechanical engineering, materials science, electrical engineering, reliability engineering and risk management.

Автор: Carlos A. Coelho; Barry C. Arnold
Название: Finite Form Representations for Meijer G and Fox H Functions
ISBN: 3030287890 ISBN-13(EAN): 9783030287894
Издательство: Springer
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Цена: 13974.00 р.
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Описание: This book depicts a wide range of situations in which there exist finite form representations for the Meijer G and the Fox H functions. Accordingly, it will be of interest to researchers and graduate students who, when implementing likelihood ratio tests in multivariate analysis, would like to know if there exists an explicit manageable finite form for the distribution of the test statistics. In these cases, both the exact quantiles and the exact p-values of the likelihood ratio tests can be computed quickly and efficiently.The test statistics in question range from common ones, such as those used to test e.g. the equality of means or the independence of blocks of variables in real or complex normally distributed random vectors; to far more elaborate tests on the structure of covariance matrices and equality of mean vectors. The book also provides computational modules in Mathematica®, MAXIMA and R, which allow readers to easily implement, plot and compute the distributions of any of these statistics, or any other statistics that fit into the general paradigm described here.

Автор: Adcock, Ben Brugiapaglia, Simone Webster, Clayton G.
Название: Sparse polynomial approximation of high-dimensional functions
ISBN: 1611976871 ISBN-13(EAN): 9781611976878
Издательство: Mare Nostrum (Eurospan)
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Описание: Over seventy years ago, Richard Bellman coined the term "the curse of dimensionality" to describe phenomena and computational challenges that arise in high dimensions. These challenges, in tandem with the ubiquity of high-dimensional functions in real-world applications, have led to a lengthy, focused research effort on high-dimensional approximation—that is, the development of methods for approximating functions of many variables accurately and efficiently from data. This book provides an in-depth treatment of one of the latest installments in this long and ongoing story: sparse polynomial approximation methods. These methods have emerged as useful tools for various high-dimensional approximation tasks arising in a range of applications in computational science and engineering. It begins with a comprehensive overview of best s-term polynomial approximation theory for holomorphic, high-dimensional functions, as well as a detailed survey of applications to parametric differential equations. It then describes methods for computing sparse polynomial approximations, focusing on least squares and compressed sensing techniques.Sparse Polynomial Approximation of High-Dimensional Functions presents the first comprehensive and unified treatment of polynomial approximation techniques that can mitigate the curse of dimensionality in high-dimensional approximation, including least squares and compressed sensing. It develops main concepts in a mathematically rigorous manner, with full proofs given wherever possible, and it contains many numerical examples, each accompanied by downloadable code. The authors provide an extensive bibliography of over 350 relevant references, with an additional annotated bibliography available on the book's companion website (www.sparse-hd-book.com).This text is aimed at graduate students, postdoctoral fellows, and researchers in mathematics, computer science, and engineering who are interested in high-dimensional polynomial approximation techniques.