A New Class of Analysis-Based Fast Transforms

ISBN-13: 9783838309279 / Angielski / Miękka / 2009 / 100 str.

Michael O'Neil

Opis

This book introduces a new approach to the rapid numerical application of certain types of linear operators to arbitrary vectors. The scheme is applicable to many classical integral transforms, and to the expansions associated with most families of classical special functions, including, among others, Bessel functions, Legendre, Hermite, and Laguerre polynomials, Spherical Harmonics, and Prolate Spheroidal Wave functions. Calculations of this type are encountered in geophysical modeling, submarine warfare, quantum mechanical calculations, and simulation of radar phenomena. The performance of the algorithm is illustrated via a number of numerical examples. The material presented in this book assumes a working knowledge of linear algebra and calculus. Graduate level students and practitioners in the fields of scientific computing, numerical linear algebra, and mathematical physics will find this book useful.

O autorze

Michael O'Neil received his B.A. in Mathematics from Cornell University in 2003, and his Ph.D. in Applied Mathematics from Yale University in 2007. His research interests include scientific computing, numerical solutions to integral equations, and numerical linear algebra.