Numerical methods and software:
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Englewood Cliffs, NJ
Prentice Hall
1989
|
| Schriftenreihe: | Prentice Hall series in computational mathematics
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001513482&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XII, 495 S. Ill., graph. Darst. 1 Diskette 5.25" |
| ISBN: | 0136272584 |
Internformat
MARC
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0001 91 A 9200 0102 MAT 650f 2001 A 20040 0102 MAT 650f 2001 A 20039 |
|---|---|
| DE-BY-TUM_katkey | 390887 |
| DE-BY-TUM_location | Mag 01 |
| DE-BY-TUM_media_number | 040000732683 040010563703 040020495303 |
| _version_ | 1821937015406460928 |
| adam_text | CONTENTS
Acknowledgments xi
7 Introduction 7
1.1 WHY A NEW BOOK? 1
1.2 THE SUBROUTINES 4
1.3 MATHEMATICAL SOFTWARE—AN EXAMPLE:
SQUARE ROOT OF SUM OF SQUARES 7
1.4 PORTABILITY 9
1.5 SOFTWARE DESIGN: ERROR HANDLING 10
1.6 SOFTWARE DESIGN: SCRATCH STORAGE 11
1.7 HISTORICAL PERSPECTIVE: BACKUS AND THE
FORTRAN LANGUAGE 12
1.8 OTHER USEFUL SOURCES OF INFORMATION 13
1.9 PROBLEMS 15
2 Computer Arithmetic and Computational Errors 17
2.1 INTRODUCTION 17
2.2 REPRESENTATION OF NUMBERS 21
2.3 MACHINE CONSTANTS 24
2.4 ERRORS IN SCIENTIFIC COMPUTING 27
*2.5 EXTRAPOLATION 31
2.6 HISTORICAL PERSPECTIVE: ECKERT AND MAUCHLY 33
2.7 PROBLEMS 35
v
vi Contents
3 Linear Systems of Equations 41
3.1 INTRODUCTION 41
3.2 LINEAR SYSTEMS FOR STORED MATRICES 44
3.3 SUBROUTINE SGEFS 54
3.4 HISTORICAL PERSPECTIVE: J.H. WILKINSON 57
3.5 COLUMN ORIENTED ALGORITHMS 59
*3.6 MORE ABOUT CONDITION NUMBERS 61
*3.7 NORMS AND ERROR ANALYSIS 66
*3.8 ESTIMATING THE CONDITION NUMBER 68
3.9 FURTHER IDEAS 70
3.10 PROBLEMS 75
3.11 PROLOGUE: SGEFS 78
4 Interpolation 81
4.1 INTRODUCTION 81
4.2 POLYNOMIAL INTERPOLATION 87
4.3 USING OTHER BASIS FUNCTIONS 89
4.4 HOW GOOD IS POLYNOMIAL INTERPOLATION? 93
4.5 HISTORIAL PERSPECTIVE: RUNGE 95
4.6 EVALUATION OF POLYNOMIALS 96
4.7 PIECEWISE LINEAR INTERPOLATION 97
4.8 PIECEWISE CUBIC FUNCTIONS 100
4.9 PCHIP, PIECEWISE CUBIC HERMITE INTERPOLATION
PACKAGE 104
*4.10 CUBIC HERMITE INTERPOLATION—DETAILS 106
4.11 CUBIC SPLINES 108
4.12 PRACTICAL DIFFERENCES BETWEEN SPLINES AND
CUBIC HERMITES 110
4.13 BEZIER CURVES 114
*4.14 B SPLINES 120
4.15 PROBLEMS 125
4.16 PROLOGUES: PCHEZ AND PCHEV 133
5 Numerical Quadrature 138
5.1 INTRODUCTION 138
5.2 ONE DIMENSIONAL QUADRATURE RULES AND
FORMULAS 140
5.3 CHANGE OF INTERVAL 148
5.4 COMPOUND QUADRATURE RULES AND ERROR
ESTIMATES 149
5.5 GAUSS KRONROD QUADRATURE RULES 153
5.6 AUTOMATIC AND ADAPTIVE QUADRATURE
ALGORITHMS 155
5.7 SUBROUTINES QIDA AND QKI5 157
5.8 DATA INTEGRATION 160
5.9 INFINITE AND SEMI INFINITE INTERVALS 163
*5.10 DOUBLE INTEGRALS 169
5.11 MONTE CARLO METHODS 176
5.12 HISTORICAL PERSPECTIVE: ULAM (1909 1984) AND
VON NEUMANN (1903 1957) 179
5.13 PROBLEMS 181
5.14 PROLOGUES: QK15, Q1 DA, AND PCHQA 184
Contents vii
6 Linear Least Squares Data Fitting 190
6.1 INTRODUCTION 190
6.2 EXPLORING DATA 196
6.3 THE NORMAL EQUATIONS 201
6.4 ORTHOGONAL FACTORIZATIONS 203
6.5 SUBROUTINE SQRLS 210
6.6 HISTORICAL PERSPECTIVE: GAUSS 212
*6.7 DEGENERATE LEAST SQUARES PROBLEMS 214
*6.8 THE SINGULAR VALUE DECOMPOSITION 218
*6.9 THE NULL SPACE PROBLEM 223
6.10 PROBLEMS 226
6.11 PROLOGUE: SQRLS 231
7 Solution of Nonlinear Equations 235
7.1 INTRODUCTION 235
7.2 METHODS FOR COMPUTING REAL ROOTS 239
7.3 SUBROUTINE FZERO 248
7.4 HISTORICAL PERSPECTIVE: EVARISTE GALOIS 251
7.5 SYSTEMS OF NONLINEAR EQUATIONS 253
7.6 SUBROUTINE SNSQE 258
7.7 PROBLEMS 260
7.8 PROLOGUES: FZERO AND SNSQE 264
8 Ordinary Differential Equations 272
8.1 INTRODUCTION 272
8.2 STABLE AND UNSTABLE EQUATIONS, NUMERICAL
METHODS 280
8.3 STIFF DIFFERENTIAL EQUATIONS 284
8.4 EULER S METHOD 285
8.5 ACCURACY AND STABILITY OF NUMERICAL
METHODS 287
8.6 ORDER OF AN INTEGRATION METHOD 294
8.7 SUBROUTINE SDRIV2 295
8.8 IMPLICIT METHODS 298
8.9 MULTI STEP METHODS 303
*8.10 ORDER AND ERROR OF A MULTI STEP METHOD
304
8.11 STABILITY FOR MULTI STEP METHODS 306
*8.12 FUNCTIONAL ITERATION AND NEWTON S METHOD
FOR SOLVING THE IMPLICIT EQUATIONS 306
*8.13 OZONE IN THE ATMOSPHERE—A STIFF SYSTEM
311
8.14 MULTI VALUE METHODS 314
8.15 AN EXAMPLE OF MULTI VALUE 317
8.16 OTHER MULTI VALUE METHODS 319
8.17 RELATION OF MULTI STEP AND MULTI VALUE
METHODS 321
*8.18 ATTRACTIVE CHARACTERISTICS OF MULTI VALUE:
STEP SIZE AND ORDER CHANGING 322
*8.19 TAYLOR SERIES AND RUNGE KUTTA METHODS 325
viii Contents
*8.20 SOME TOPICS OMITTED 329
8.21 PROBLEMS 331
8.22 PROLOGUE: SDRIV2 341
9 Optimization and Nonlinear Least Squares 347
9.1 INTRODUCTION 347
9.2 ONE DIMENSIONAL OPTIMIZATION 350
9.3 SUBROUTINE FMIN 361
9.4 OPTIMIZATION IN MANY DIMENSIONS 363
9.5 SUBROUTINE UNCMIN 370
9.6 NONLINEAR DATA FITTING 372
9.7 HISTORICAL PERSPECTIVE: SIR ISAAC NEWTON
(1642 1727) 374
9.8 FURTHER IDEAS 376
9.9 PROBLEMS 377
9.10 PROLOGUES: FMIN AND UNCMIN 381
10 Simulation and Random Numbers 385
10.1 INTRODUCTION 385
10.2 RANDOM NUMBERS 387
10.3 GENERATION OF UNIFORMLY DISTRIBUTED
NUMBERS 389
10.4 APPLICATIONS OF RANDOM NUMBERS:
BROWNIAN MOTION AND FRACTALS 392
10.5 CONGRUENTIAL AND FIBONACCI
GENERATORS 395
10.6 FUNCTION UNI 397
10.7 SAMPLING FROM OTHER DISTRIBUTIONS 397
10.8 FUNCTION RNOR 400
*10.9 EXAMPLE: RADIATION SHIELDING AND REACTOR
CRITICALITY 403
10.10 PROBLEMS 404
10.11 PROLOGUES: UNI AND RNOR 410
7 7 Trigonometric Approximation and the Fast 413
Fourier Transform
11.1 INTRODUCTION 413
11.2 FOURIER INTEGRAL TRANSFORM, DISCRETE
FOURIER TRANSFORM, AND FOURIER
SERIES 414
11.3 ENERGY AND POWER 417
11.4 HISTORICAL PERSPECTIVE: FOURIER
(1786 1830) 421
11.5 PRACTICAL COMPUTATION OF FOURIER
COEFFICIENTS; THE DISCRETE FOURIER
TRANSFORM 422
11.6 SUBROUTINES EZFFTF AND EZFFTB 427
Contents ix
11.7 TRUNCATED FOURIER SERIES AS AN
APPROXIMATION 430
11.8 RELATIONSHIPS BETWEEN FOURIER
TRANSFORMS AND FOURIER SERIES 437
11.9 LEAST SQUARES APPLICATIONS: EL Nl NO 441
11.10 THE FAST FOURIER TRANSFORM 445
*11.11 COMPLEX REPRESENTATION 448
*11.12 TWO DIMENSIONAL TRANSFORMS 454
*11.13 CONVOLUTION AND CORRELATION 458
11.14 HISTORICAL PERSPECTIVE: THE FAST FOURIER
TRANSFORM 465
11.15 PROBLEMS 466
11.16 PROLOGUES: EZFFTF, EZFFTB, CFFTF, CFFTB AND
CFFT2D 470
Bibliography 476
Index 483
|
| any_adam_object | 1 |
| author | Kahaner, David K. Moler, Cleve B. 1939- Nash, Stephen G. |
| author_GND | (DE-588)107887975 (DE-588)128553634 |
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| discipline | Physik Informatik Mathematik |
| format | Book |
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| id | DE-604.BV002302853 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T07:49:11Z |
| institution | BVB |
| isbn | 0136272584 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001513482 |
| oclc_num | 630749034 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-20 DE-83 DE-188 |
| owner_facet | DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-20 DE-83 DE-188 |
| physical | XII, 495 S. Ill., graph. Darst. 1 Diskette 5.25" |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Prentice Hall |
| record_format | marc |
| series2 | Prentice Hall series in computational mathematics |
| spellingShingle | Kahaner, David K. Moler, Cleve B. 1939- Nash, Stephen G. Numerical methods and software Programmierung (DE-588)4076370-5 gnd Ingenieurmathematik Programm (DE-588)4281847-3 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Software (DE-588)4055382-6 gnd Computerarithmetik (DE-588)4135485-0 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4076370-5 (DE-588)4281847-3 (DE-588)4128130-5 (DE-588)4055382-6 (DE-588)4135485-0 (DE-588)4042805-9 |
| title | Numerical methods and software |
| title_auth | Numerical methods and software |
| title_exact_search | Numerical methods and software |
| title_full | Numerical methods and software David Kahaner ; Cleve Moler ; Stephen Nash |
| title_fullStr | Numerical methods and software David Kahaner ; Cleve Moler ; Stephen Nash |
| title_full_unstemmed | Numerical methods and software David Kahaner ; Cleve Moler ; Stephen Nash |
| title_short | Numerical methods and software |
| title_sort | numerical methods and software |
| topic | Programmierung (DE-588)4076370-5 gnd Ingenieurmathematik Programm (DE-588)4281847-3 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Software (DE-588)4055382-6 gnd Computerarithmetik (DE-588)4135485-0 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Programmierung Ingenieurmathematik Programm Numerisches Verfahren Software Computerarithmetik Numerische Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001513482&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kahanerdavidk numericalmethodsandsoftware AT molercleveb numericalmethodsandsoftware AT nashstepheng numericalmethodsandsoftware |
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Bibliotheksmagazin
| Signatur: |
0001 91 A 9200
Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |
Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 650f 2001 A 20039
Lageplan 0102 MAT 650f 2001 A 20040 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |
| Exemplar 2 | Ausleihbar Am Standort |