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### Table of contents

#### Actions for selected chapters

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#### INTRODUCTION

J.F. Traub

Pages 1-4 - Book chapterAbstract only
#### SOME REMARKS ON PROOF TECHNIQUES IN ANALYTIC COMPLEXITY

S. Winograd

Pages 5-14 - Book chapterAbstract only
#### STRICT LOWER AND UPPER BOUNDS ON ITERATIVE COMPUTATIONAL COMPLEXITY

J.F. Traub and H. Woźniakowski

Pages 15-34 - Book chapterAbstract only
#### THE COMPLEXITY OF OBTAINING STARTING POINTS FOR SOLVING OPERATOR EQUATIONS BY NEWTON'S METHOD

H.T. Kung

Pages 35-57 - Book chapterAbstract only
#### A CLASS OF OPTIMAL-ORDER ZERO-FINDING METHODS USING DERIVATIVE EVALUATIONS

Richard P. Brent

Pages 59-73 - Book chapterAbstract only
#### MAXIMAL ORDER OF MULTIPOINT ITERATIONS USING n EVALUATIONS

H. Woźniakowski

Pages 75-107 - Book chapterAbstract only
#### OPTIMAL USE OF INFORMATION IN CERTAIN ITERATIVE PROCESSES

Robert MEERSMAN

Pages 109-125 - Book chapterAbstract only
#### THE USE OF INTEGRALS IN THE SOLUTION OF NONLINEAR EQUATIONS IN N DIMENSIONS

B. Kacewicz

Pages 127-141 - Book chapterAbstract only
#### Complexity and Differential Equations

M.H. SCHULTZ

Pages 143-149 - Book chapterAbstract only
#### MULTIPLE-PRECISION ZERO-FINDING METHODS AND THE COMPLEXITY OF ELEMENTARY FUNCTION EVALUATION

Richard P. Brent

Pages 151-176 - Book chapterAbstract only
#### NUMERICAL STABILITY OF ITERATIONS FOR SOLUTION OF NONLINEAR EQUATIONS AND LARGE LINEAR SYSTEMS

H. Woźniakowski

Pages 177-190 - Book chapterAbstract only
#### ON THE COMPUTATIONAL COMPLEXITY OF APPROXIMATION OPERATORS II

JOHN R. RICE

Pages 191-204 - Book chapterAbstract only
#### HENSEL MEETS NEWTON — ALGEBRAIC CONSTRUCTIONS IN AN ANALYTIC SETTING

DAVID Y.Y. YUN

Pages 205-215 - Book chapterAbstract only
#### O((n log n)

^{3/2}) ALGORITHMS FOR COMPOSITION AND REVERSION OF POWER SERIESRichard P. Brent and H.T. Kung

Pages 217-225

## About the book

### 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.

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.

## Details

### ISBN

978-0-12-697560-4

### Language

English

### Published

1976

### Copyright

Copyright © 1976 Elsevier Inc. All rights reserved.

### Imprint

Academic Press