Symbolic Asymptotics
By: by John R. Shackell
Series: Algorithms and Computation in Mathematics -- 12; Algorithms and Computation in Mathematics -- 12
Publisher: Springer Berlin Heidelberg
Published: 2004
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 243
ISBN-13: 9783642059254; 9783662101766
Subjects: Algorithms; Computer science; Data processing; Algebra; Mathematics; Global analysis (Mathematics)
Description: Symbolic asymptotics has recently undergone considerable theoretical development, especially in areas where power series are no longer an appropriate tool. Implementation is beginning to follow. The present book, written by one of the leading specialists in the area, is currently the only one to treat this part of symbolic asymptotics. It contains a good deal of interesting material in a new, developing field of mathematics at the intersection of algebra, analysis and computing, presented in a lively and readable way. The associated areas of zero equivalence and Hardy fields are also covered. The book is intended to be accessible to anyone with a good general background in mathematics, but it nonetheless gets right to the cutting edge of active research. Some results appear here for the first time, while others have hitherto only been given in preprints. Due to its clear presentation, this book is interesting for a broad audience of mathematicians and theoretical computer scientists.
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Table of contents: title: Introduction; title: Zero Equivalence; title: Hardy Fields; title: Output Data Structures; title: Algorithms for Function Towers; title: Algebraic Differential Equations; title: Inverse Functions; title: Implicit Functions; title: Star-Product Expansions; title: Oscillating Functions; title: References; title: Index.