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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis
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Sparse Polynomial Approximation of High-Dimensional Functions (Paperback)
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Sparse Polynomial Approximation of High-Dimensional Functions (Paperback)
Series: Computational Science and Engineering
Expected to ship within 10 - 15 working days
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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.
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