Analytic Computational Complexity - 1st Edition - ISBN: 9780126975604, 9781483257891

Analytic Computational Complexity

1st Edition

Editors: J.F. Traub
eBook ISBN: 9781483257891
Imprint: Academic Press
Published Date: 28th January 1976
Page Count: 250
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Analytic Computational Complexity contains the proceedings of the Symposium on Analytic Computational Complexity held by the Computer Science Department, Carnegie-Mellon University, Pittsburgh, Pennsylvania, on April 7-8, 1975. The symposium provided a forum for assessing progress made in analytic computational complexity and covered topics ranging from strict lower and upper bounds on iterative computational complexity to numerical stability of iterations for solution of nonlinear equations and large linear systems.

Comprised of 14 chapters, this book begins with an introduction to analytic computational complexity before turning to proof techniques used in analytic complexity. Subsequent chapters focus on the complexity of obtaining starting points for solving operator equations by Newton's method; maximal order of multipoint iterations using n evaluations; the use of integrals in the solution of nonlinear equations in N dimensions; and the complexity of differential equations. Algebraic constructions in an analytic setting are also discussed, along with the computational complexity of approximation operators.

This monograph will be of interest to students and practitioners in the fields of applied mathematics and computer science.

Table of Contents

List of Invited Authors



Some Remarks on Proof Techniques in Analytic Complexity

Strict Lower and Upper Bounds on Iterative Computational Complexity

The Complexity of Obtaining Starting Points for Solving Operator Equations by Newton's Method

A Class of Optimal-Order Zero-Finding Methods Using Derivative Evaluations

Maximal Order of Multipoint Iterations Using n Evaluations

Optimal Use of Information in Certain Iterative Processes

The Use of Integrals in the Solution of NonUnear Equations in N Dimensions

Complexity and Differential Equations

Multiple-Precision Zero-Finding Methods and the Complexity of Elementary Function Evaluation

Numerical Stability of Iterations for Solution of Nonlinear Equations, and Large Linear Systems

On the Computational Complexity of Approximation Operators II

Hensel Meets Newton-Algebraic Constructions in an Analytic Setting

Ο((n Log n)3/2) Algorithms for Composition and Reversion of Power Series

Abstracts of Contributed Papers


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© Academic Press 1976
Academic Press
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About the Editor

J.F. Traub

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