Complexity and Real Computation (Hardcover, 1998 ed.)

The classical theory of computation has its origins in the work of Goedel, Turing, Church, and Kleene and has been an extraordinarily successful framework for theoretical computer science. The thesis of this book, however, is that it provides an inadequate foundation for modern scientific computation where most of the algorithms are real number algorithms. The goal of this book is to develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing. Along the way, the authors consider such fundamental problems as: * Is the Mandelbrot set decidable? * For simple quadratic maps, is the Julia set a halting set? * What is the real complexity of Newton's method? * Is there an algorithm for deciding the knapsack problem in a ploynomial number of steps? * Is the Hilbert Nullstellensatz intractable? * Is the problem of locating a real zero of a degree four polynomial intractable? * Is linear programming tractable over the reals? The book is divided into three parts: The first part provides an extensive introduction and then proves the fundamental NP-completeness theorems of Cook-Karp and their extensions to more general number fields as the real and complex numbers. The later parts of the book develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing.

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Release date:	October 1997
First published:	1998
Authors:	Lenore Blum • Felipe Cucker • Michael Shub • Steve Smale
Dimensions:	235 x 155 x 32mm (L x W x T)
Format:	Hardcover
Pages:	453
Edition:	1998 ed.
ISBN-13:	978-0-387-98281-6
Categories:	Books > Computing & IT > General theory of computing > Mathematical theory of computation Books > Science & Mathematics > Mathematics > Mathematical foundations > Mathematical logic
LSN:	0-387-98281-7
Barcode:	9780387982816

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