Analytic Computational Complexity

Analytic Computational Complexity

1st Edition - January 28, 1976

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  • Editor: J.F. Traub
  • eBook ISBN: 9781483257891

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Description

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

    Preface

    Introduction

    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

Product details

  • No. of pages: 250
  • Language: English
  • Copyright: © Academic Press 1976
  • Published: January 28, 1976
  • Imprint: Academic Press
  • eBook ISBN: 9781483257891

About the Editor

J.F. Traub

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