Libro Análisis Real
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Publicado: 10 de mayo de 2012
title author publisher isbn10 | asin print isbn13 ebook isbn13 language subject publication date lcc ddc subject
: : : : : : : : : : : cover Page iii
Numerical Methods in Economics Kenneth L. Judd The MIT Press Cambridge, Massachusetts London, England page_iii Page iv © 1998 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by anyelectronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. This book was set in Times New Roman on the Monotype "Prism Plus" PostScript Imagesetter by Asco Trade Typesetting Ltd., Hong Kong. Printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Judd,Kenneth L. Numerical methods in economics / Kenneth L. Judd. p. cm. Includes bibliographical references (p. ) and index. ISBN 0-262-10071-1 (hc) 1. EconomicStatistical methods. I. Title HB137.J83 1998 330'.01'5195dc21 98-13591 CIP page_iv
Page v
Dedicated to the memory of Joyce Lewis Judd page_v Page vii
CONTENTS Preface I Introduction 1 Introduction xv 1
3
1.1 What Economists CanCompute
3
1.2 Roles of Computation in Economic Analysis
6
1.3 Computation in Science
13
1.4 Future of Computing
15
1.5 Objectives and Nature of This Book
17
1.6 Basic Mathematics, Notation, and Terminology
20
1.7 Software and Supplemental Material
25
1.8 Further Reading
26
Exercises 2 Elementary Concepts in Numerical Analysis
27
29
2.1 ComputerArithmetic
29
2.2 Computer Processing and Algorithms
31
2.3 Economics of Computation
33
2.4 Efficient Polynomial Evaluation
34
2.5 Efficient Computation of Derivatives
35
2.6 Direct versus Iterative Methods
39
2.7 Error: The Central Problem of Numerical Mathematics
39
2.8 Making Infinite Sequences Finite
41
2.9 Methods of Approximation
44
2.10Evaluating the Error in the Final Result
45
2.11 Computational Complexity
48
2.12 Further Reading and Summary
50
Exercises II Basics from Numerical Analysis on Rn 3 Linear Equations and Iterative Methods
50
53
55
3.1 Gaussian Elimination, LU Decomposition
55
3.2 Alternative Methods
58
3.3 Banded Sparse Matrix Methods
61
3.4 General Sparse MatrixMethods page_vii
62
Page viii 3.5 Error Analysis 66
3.6 Iterative Methods
70
3.7 Operator Splitting Approach
75
3.8 Convergence of Iterative Schemes
77
3.9 Acceleration and Stabilization Methods
78
3.10 Calculating A-1
84
3.11 Computing Ergodic Distributions
85
3.12 Overidentified Systems
88
3.13 Software
88
3.14 Further Reading and Summary89
Exercises 4 Optimization
89
93
4.1 One-Dimensional Minimization
94
4.2 Multidimensional Optimization: Comparison Methods
99
4.3 Newton's Method for Multivariate Problems
103
4.4 Direction Set Methods
109
4.5 Nonlinear Least Squares
117
4.6 Linear Programming
120
4.7 Constrained Nonlinear Optimization
121
4.8 Incentive Problems
128
4.9Computing Nash Equilibrium
133
4.10 A Portfolio Problem
135
4.11 A Simple Econometric Example
137
4.12 A Dynamic Optimization Problem
140
4.13 Software
142
4.14 Further Reading and Summary
142
Exercises 5 Nonlinear Equations
143
147
5.1 One-Dimensional Problems: Bisection
147
5.2 One-Dimensional Problems: Newton's Method
150
5.3 SpecialMethods for One-Dimensional Problems
158
5.4 Elementary Methods for Multivariate Nonlinear Equations
159
5.5 Newton's Method for Multivariate Equations
167
5.6 Methods That Enhance Global Convergence
171
5.7 Advantageous Transformations page_viii
174
Page ix 5.8 A Simple Continuation Method 176
5.9 Homotopy Continuation Methods
179
5.10 A Simple CGE Problem...
: : : : : : : : : : : cover Page iii
Numerical Methods in Economics Kenneth L. Judd The MIT Press Cambridge, Massachusetts London, England page_iii Page iv © 1998 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by anyelectronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. This book was set in Times New Roman on the Monotype "Prism Plus" PostScript Imagesetter by Asco Trade Typesetting Ltd., Hong Kong. Printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Judd,Kenneth L. Numerical methods in economics / Kenneth L. Judd. p. cm. Includes bibliographical references (p. ) and index. ISBN 0-262-10071-1 (hc) 1. EconomicStatistical methods. I. Title HB137.J83 1998 330'.01'5195dc21 98-13591 CIP page_iv
Page v
Dedicated to the memory of Joyce Lewis Judd page_v Page vii
CONTENTS Preface I Introduction 1 Introduction xv 1
3
1.1 What Economists CanCompute
3
1.2 Roles of Computation in Economic Analysis
6
1.3 Computation in Science
13
1.4 Future of Computing
15
1.5 Objectives and Nature of This Book
17
1.6 Basic Mathematics, Notation, and Terminology
20
1.7 Software and Supplemental Material
25
1.8 Further Reading
26
Exercises 2 Elementary Concepts in Numerical Analysis
27
29
2.1 ComputerArithmetic
29
2.2 Computer Processing and Algorithms
31
2.3 Economics of Computation
33
2.4 Efficient Polynomial Evaluation
34
2.5 Efficient Computation of Derivatives
35
2.6 Direct versus Iterative Methods
39
2.7 Error: The Central Problem of Numerical Mathematics
39
2.8 Making Infinite Sequences Finite
41
2.9 Methods of Approximation
44
2.10Evaluating the Error in the Final Result
45
2.11 Computational Complexity
48
2.12 Further Reading and Summary
50
Exercises II Basics from Numerical Analysis on Rn 3 Linear Equations and Iterative Methods
50
53
55
3.1 Gaussian Elimination, LU Decomposition
55
3.2 Alternative Methods
58
3.3 Banded Sparse Matrix Methods
61
3.4 General Sparse MatrixMethods page_vii
62
Page viii 3.5 Error Analysis 66
3.6 Iterative Methods
70
3.7 Operator Splitting Approach
75
3.8 Convergence of Iterative Schemes
77
3.9 Acceleration and Stabilization Methods
78
3.10 Calculating A-1
84
3.11 Computing Ergodic Distributions
85
3.12 Overidentified Systems
88
3.13 Software
88
3.14 Further Reading and Summary89
Exercises 4 Optimization
89
93
4.1 One-Dimensional Minimization
94
4.2 Multidimensional Optimization: Comparison Methods
99
4.3 Newton's Method for Multivariate Problems
103
4.4 Direction Set Methods
109
4.5 Nonlinear Least Squares
117
4.6 Linear Programming
120
4.7 Constrained Nonlinear Optimization
121
4.8 Incentive Problems
128
4.9Computing Nash Equilibrium
133
4.10 A Portfolio Problem
135
4.11 A Simple Econometric Example
137
4.12 A Dynamic Optimization Problem
140
4.13 Software
142
4.14 Further Reading and Summary
142
Exercises 5 Nonlinear Equations
143
147
5.1 One-Dimensional Problems: Bisection
147
5.2 One-Dimensional Problems: Newton's Method
150
5.3 SpecialMethods for One-Dimensional Problems
158
5.4 Elementary Methods for Multivariate Nonlinear Equations
159
5.5 Newton's Method for Multivariate Equations
167
5.6 Methods That Enhance Global Convergence
171
5.7 Advantageous Transformations page_viii
174
Page ix 5.8 A Simple Continuation Method 176
5.9 Homotopy Continuation Methods
179
5.10 A Simple CGE Problem...
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