Numerical methods for engineers and computer scientists:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Menlo Park [u.a.]
Benjamin, Cummings
1988
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 326 S. graph. Darst. |
| ISBN: | 080534652X |
Internformat
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Datensatz im Suchindex
| DE-BY-862_location | 2801 |
|---|---|
| DE-BY-FWS_call_number | 2801/1991:3400 |
| DE-BY-FWS_katkey | 48611 |
| DE-BY-FWS_media_number | 083100401937 |
| _version_ | 1806195652975132672 |
| adam_text | IMAGE 1
NUMERICAL METHODS
FOR ENGINEERS AND COMPUTER SCIENTISTS
PAUL F HULTQUIST UNIVERSITY OF COLORADO AT DENVER
S
THE BENJAMIN/CUMMINGS PUBLISHING COMPANY, INC. MENLO PARK, CALIFORNIA *
READING, MASSACHUSETTS DON MILLS, ONTARIO * WOKINGHAM, U.K. * AMSTERDAM
* SYDNEY SINGAPORE * TOKYO * MADRID * BOGOTA * SANTIAGO * SAN JUAN
IMAGE 2
CONTENTS
CHAPTER 1 NUMBERS AND THEIR REPRESENTATIONS 1.1
1.2
1.3 1.4 1.5 1.6
NUMBER BASES 1 1.1.1 CONVERSION AMONG BASES 2 1.1.2 DECIMAL, BINARY,
OCTAL, AND HEXADECIMAL 4 NUMBER REPRESENTATION 6
1.2.1 INTEGER REPRESENTATION 6 1.2.2 FLOATING-POINT REPRESENTATION 8
REPRESENTATION OF DATA 10 OPERATIONS IN FLOATING-POINT 10 DOUBLE
PRECISION MODE 12 COMPLEX MODE 13
EXERCISES, 14; PROBLEMS, 16
CHAPTER 2 ERRORS AND MISTAKES
2.1 DEFINITION OF ERROR 18 2.2 SOURCES OF ERROR IN NUMBERS 19 2.2.1
INAECURATE DATA 19 2.2.2 DATAENTRY 20
2.2.3 ARITHMETIC OPERATIONS 20 2.2.4 FORMULA ERRORS 20
18
IMAGE 3
X CONTENTS
2.3 ROUND-OFF ERRORS 20
2.4 SIGNIFICANT DIGITS 21
2.5 COMPUTATION WITH DATA 23 2.6 TRUNCATION ERRORS AND ERRORS IN
FORMULAS 26 2.7 TESTING FOR EQUALITY 28
2.8 HOW TO SOLVE A QUADRATIC EQUATION 29 EXERCISES, 30
CHAPTER 3 SOFTWARE
3.1 HIGH-LEVEL LANGUAGES 33 3.2 EFFICIENCY VERSUS READABILITY 35 3.3
WRITING GOOD PROGRAMS 36 3.3.1 PROGRAMMING STYLE 36
3.3.2 DOCUMENTATION 37
3.3.3 TESTING 38
3.3.4 SPECIAL CASES 39
3.4 USE OF LIBRARIES 40
3.4.1 IMSL 41
3.4.2 LINPACK 41 3.4.3 OTHER LIBRARIES 41 PROBLEMS, 42
CHAPTER 4 SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS
4.1 INTRODUCTION 44
4.2 REVIEW OF MATRIX ALGEBRA 47
4.2.1 UNARY OPERATIONS 47
4.2.2 BINARY OPERATIONS 48 4.2.3 INVERSE OF A MATRIX 50 4.2.4 VECTOR AND
MATRIX NOR MS 50 4.3 GAUSS ELIMINATION 51
4.4 GAUSS-TPRDAN METHOD AND OPERATIONS COUNT 53 4.5 SOURCES OF TROUBLE
55 4.6 EQUILIBRATION 56
4.7 CONDITION 57
IMAGE 4
CONTENTS
4.8 ESTIMATING K(A) 62
4.9 ITERATIVE IMPROVEMENT 62 4.10 PROCEDURES GAUSS AND SOLVE 63
4.11 PROCEDURES TRIDIAG AND PENTDIAG 64 4.12 SOME IMSL SUBROUTINES 68
4.13 LINPACK PROGRAMS 69 4.14 ITERATIVE METHODS 71 EXERCISES, 73;
PROBLEMS, 74; LISTINGS, 77
CHAPTER 5 SOLUTIONS OF NONLINEAR EQUATIONS
5.1 ITERATION 87
5.2 INTERVAL HALVING 88
5.3 METHOD OF SUCCESSIVE SUBSTITUTION 91
5.4 RATE OF CONVERGENCE 94 5.5 TERMINATING THE ITERATIVE PROCESS 94
5.6 NEWTON S METHOD 96 5.7 TWO-POINT FORMULAS 100 5.8 ACCELERATING
CONVERGENCE 101 5.9 PRACTICAL CONSIDERATIONS 102
5.10 POLYNOMIAL EQUATIONS 104 5.10.1 TWO-DIMENSIONAL NEWTON S METHOD 105
5.10.2 OTHER METHODS FOR POLYNOMIALS 106 5.10.3 STABILITY OF
ROOT-FINDING PROCESSES 106
5.11 FUNCTION ZEROIN 107 5.12 BAIRSTOW S METHOD 108
5.13 IMSL ROUTINE ZBRENT 109 5.14 IMSL ROUTINE ZRPOLY 110 EXERCISES,
111; PROBLEMS, 114; LISTINGS, 120
86
CHAPTER 6 FITTING CURVES TO DATA
6.1 PRELIMINARIES 130 6.2 FUNCTIONS AND CONTINUITY 131
6.3 INTERPOLATION 131 6.3.1 LAGRANGE INTERPOLATION POLYNOMIALS 133
128
IMAGE 5
XII CONTENTS
6.3.2 DIFFERENCE METHODS 135
6.4 SPLINES 144
6.4.1 NATURAL SPLINE 145 6.4.2 OTHER SPLINES 148 6.4.3 PROCEDURE
CUBIC-SPLINE AND FUNCTION SPLEVAL 148 6.5 LEAST SQUARES 149
6.5.1 LINEAR REGRESSION 149
6.5.2 MULTIPLE REGRESSION 153 6.5.3 NONLINEAR REGRESSION 155 6.5.4
ORTHOGONAL POLYNOMIALS 157 6.5.5 ORTHOGONAL POLYNOMIAL ROUTINES 159
6.5.6 OTHER KINDS OF EQUATIONS 164 EXERCISES, 167; PROBLEMS, 172;
LISTINGS, 177
CHAPTER 7 NUMERICAL EVALUATION OF INTEGRALS
7.1 INTRODUCTION 189 7.2 THE DEFINITE INTEGRAL 191 7.3 NEWTON-COTES
CLOSED FORMULAS 192 7.4 NEWTON-COTES OPEN FORMULAS 196
7.5 STEP SIZE AND ACCURACY 197 7.5.1 SIMPLE INTEGRATOR WITH ERROR
ESTIMATE 200 7.6 ROMBERG INTEGRATION 202
7.7 GAUSS QUADRATURE 204 7.7.1 GAUSS-LEGENDRE QUADRATURE 205 7.7.2
GAUSS-CHEBYSHEV QUADRATURE 210 7.7.3 GAUSS-LAGUERRE QUADRATURE 211
7.7.4 GAUSS-HERMITE QUADRATURE 213
7.7.5 ERROR TERMS 214
7.8 ADAPTIVE QUADRATURE 215 7.9 DEALING WITH SINGULARITIES 218 7.10 IMSL
FUNCTION DCADRE 220 EXERCISES, 221; PROBLEMS, 224; LISTINGS, 228
CHAPTER 8 NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS
8.1 DIFFERENTIAL EQUATIONS AND SYSTEMS 238 8.2 METHODS OF SOLUTION 241
IMAGE 6
CONTENTS XIII
8.2.1 MORE SOPHISTICATED METHODS: MULTISTEP 245
8.2.2 MULTISTEP METHODS: ERROR ESTIMATION AND STEP SIZE CONTROL 247
8.3 RUNGE-KUTTA METHODS 248 8.4 COMPARISON OF METHODS 252
8.5 SOLVING SYSTEMS OF DIFFERENTIAL EQUATIONS NUMERICALLY 252 8.6
STABILITY 255
8.7 STIFF DIFFERENTIAL EQUATIONS 257
8.8 BOUNDARY VALUE PROBLEMS 259 8.8.1 THE SHOOTING METHOD 259 8.8.2
FINITE DIFFERENCE METHOD 260
8.9 PROCEDURE RKF45 261 8.10 IMSL SUBROUTINE DVERK 263 EXERCISES, 265;
PROBLEMS, 267; LISTINGS, 273
CHAPTER 9 MATHEMATICAL FUNCTIONS 283
9.1 INTRODUCTION 283 9.1.1 STANDARD FUNCTIONS 284 9.1.2 POLYNOMIAL
APPROXIMATIONS 284
9.2 LEAST-SQUARES APPROXIMATION OF FUNCTIONS 286 9.3 CHEBYSHEV
ECONOMIZATION 288 9.4 MINIMAX APPROXIMATION: REMES ALGORITHMS 294
9.5 PROCEDURE MINIMAX 298 9.6 IMSL SUBROUTINE IRATCU 299 EXERCISES, 300;
PROBLEMS, 301; LISTINGS, 302
ANSWERS TO SELECTED EXERCISES 311 REFERENCES 315 BIBLIOGRAPHY 317
INDEX 321
|
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| indexdate | 2024-08-01T16:26:42Z |
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| isbn | 080534652X |
| language | English |
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| spellingShingle | Hultquist, Paul F. Numerical methods for engineers and computer scientists Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4042805-9 |
| title | Numerical methods for engineers and computer scientists |
| title_auth | Numerical methods for engineers and computer scientists |
| title_exact_search | Numerical methods for engineers and computer scientists |
| title_full | Numerical methods for engineers and computer scientists Paul F. Hultquist |
| title_fullStr | Numerical methods for engineers and computer scientists Paul F. Hultquist |
| title_full_unstemmed | Numerical methods for engineers and computer scientists Paul F. Hultquist |
| title_short | Numerical methods for engineers and computer scientists |
| title_sort | numerical methods for engineers and computer scientists |
| topic | Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Numerische Mathematik |
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Inhaltsverzeichnis
Schweinfurt Magazin
| Signatur: |
2801 1991:3400 |
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| Exemplar 1 | ausleihbar Verfügbar Bestellen |