Numerical algorithms with Fortran:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch Deutsch |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1996
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007349443&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XXII, 602 S. graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 3540605290 |
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Datensatz im Suchindex
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|---|---|
| DE-BY-TUM_katkey | 768160 |
| DE-BY-TUM_location | 01 07 |
| DE-BY-TUM_media_number | 040020535200 040070027993 |
| _version_ | 1821938269201367041 |
| adam_text | IMAGE 1
GISELA ENGELN-MUELLGES FRANK U H L IG
NUMERICAL ALGORITHMS
WITH FORTRAN
WITH CD-ROM WITH 46 FIGURES
J PL SPRINGER
IMAGE 2
CONTENTS
1 COMPUTER NURABERS, ERROR ANALYSIS, CONDITIONING, STABILITY OF
ALGORITHMS AND OPERATIONS COUNT 1
1.1 DEFINITION OF ERRORS 1
1.2 DECIMAL REPRESENTATION OF NUMBERS 3
1.3 SOURCES OF ERRORS 6
1.3.1 INPUT ERRORS 6
1.3.2 PROCEDURAL ERRORS 7
1.3.3 ERROR PROPAGATION AND THE CONDITION OF A PROBLEM 7
1.3.4 THE COMPUTATIONAL ERROR AND NUMERICAL STABILITY OF AN ALGORITHM 10
1.4 OPERATIONS COUNT, ET CETERA 11
2 NONLINEAR EQUATIONS IN ONE VARIABLE 13
2.1 INTRODUCTION 13
2.2 DEFINITIONS AND THEOREMS ON ROOTS 14
2.3 GENERAL ITERATION PROCEDURES 15
2.3.1 HOW TO CONSTRUCT AN ITERATIVE PROCESS 15
2.3.2 EXISTENCE AND UNIQUENESS OF SOLUTIONS 16
2.3.3 CONVERGENCE AND ERROR ESTIMATES OF ITERATIVE PROCEDURES . .. 17
2.3.4 PRACTICAL IMPLEMENTATION 20
2.4 ORDER OF CONVERGENCE OF AN ITERATIVE PROCEDURE 22
2.4.1 DEFINITIONS AND THEOREMS 22
2.4.2 DETERMINING THE ORDER OF CONVERGENCE EXPERIMENTALLY 24 2.5
NEWTON S METHOD 25
2.5.1 FINDING SIMPLE ROOTS 25
2.5.2 A DAMPED VERSION OF NEWTON S METHOD 27
2.5.3 NEWTON S METHOD FOR MULTIPLE ZEROS; A MODIFIED NEWTON S METHOD 27
IMAGE 3
XIV CONTENTS
2.6 REGULA FALSI 28
2.6.1 REGULA FALSI FOR SIMPLE ROOTS 28
2.6.2 MODIFIED REGULA FALSI FOR MULTIPLE ZEROS 30
2.6.3 SIMPLEST VERSION OF THE REGULA FALSI 30
2.7 STEFFENSEN METHOD 31
2.7.1 STEFFENSEN METHOD FOR SIMPLE ZEROS 31
2.7.2 MODIFIED STEFFENSEN METHOD FOR MULTIPLE ZEROS 31
2.8 INCLUSION METHODS 32
2.8.1 BISECTION METHOD 32
2.8.2 PEGASUS METHOD 34
2.8.3 ANDERSON-BJOERCK METHOD 36
2.8.4 THE KING AND THE ANDERSON-BJOERCK-KING METHODS, THE ILLINOIS METHOD
39
2.8.5 ZEROIN METHOD 39
2.9 EFFICIENCY OF THE METHODS AND AIDS FOR DECISION MAKING 40
3 ROOTS OF POLYNOMIALS 43
3.1 PRELIMINARY REMARKS 43
3.2 THE HORNER SCHEME 44
3.2.1 FIRST LEVEL HORNER SCHEME FOR REAL ARGUMENTS 44
3.2.2 FIRST LEVEL HORNER SCHEME FOR COMPLEX ARGUMENTS 45
3.2.3 COMPLETE HORNER SCHEME FOR REAL ARGUMENTS 47
3.2.4 APPLICATIONS 49
3.3 METHODS FOR FINDING ALL SOLUTIONS OF ALGEBRAIC EQUATIONS 49
3.3.1 PRELIMINARIES 49
3.3.2 MULLER S METHOD 51
3.3.3 BAUHUBER S METHOD 54
3.3.4 THE JENKINS-TRAUB METHOD 55
3.3.5 THE LAGUERRE METHOD 56
3.4 HINTS FOR CHOOSING A METHOD 56
4 DIRECT METHODS FOR SOLVING SYSTEMS OF LINEAR EQUATIONS .. 59
4.1 THE PROBLEM 59
4.2 DEFINITIONS AND THEORETICAL BACKGROUND 60
4.3 SOLVABILITY CONDITIONS FOR SYSTEMS OF LINEAR EQUATIONS 66
4.4 THE FACTORIZATION PRINCIPLE 67
4.5 GAUSS ALGORITHM 68
4.5.1 GAUSS ALGORITHM WITH COLUMN PIVOT SEARCH 68
IMAGE 4
CONTENTS XV
4.5.2 PIVOT STRATEGIES 72
4.5.3 COMPUTER IMPLEMENTATION OF GAUSS ALGORITHM 73
4.5.4 GAUSS ALGORITHM FOR SYSTEMS WITH SEVERAL RIGHT HAND SIDES 76 4.6
MATRIX INVERSION VIA GAUSS ALGORITHM 77
4.7 LINEAR EQUATIONS WITH SYMMETRIE STRONGLY NONSINGULAR SYSTEM MATRICES
78
4.7.1 THE CHOLESKY DECOMPOSITION 78
4.7.2 THE CONJUGATE GRADIENT METHOD 83
4.8 THE GAUSS - JORDAN METHOD 87
4.9 THE MATRIX INVERSE VIA EXCHANGE STEPS 88
4.10 LINEAR SYSTEMS WITH TRIDIAGONAL MATRICES 89
4.10.1 SYSTEMS WITH TRIDIAGONAL MATRICES 89
4.10.2 SYSTEMS WITH TRIDIAGONAL SYMMETRIE STRONGLY NONSINGULAR MATRICES
92
4.11 LINEAR SYSTEMS WITH CYCLICALLY TRIDIAGONAL MATRICES 94
4.11.1 SYSTEMS WITH A CYCLICALLY TRIDIAGONAL MATRIX 94
4.11.2 SYSTEMS WITH SYMMETRIE CYCLICALLY TRIDIAGONAL STRONGLY
NONSINGULAR MATRICES 96
4.12 LINEAR SYSTEMS WITH FIVE-DIAGONAL MATRICES 98
4.12.1 SYSTEMS WITH FIVE-DIAGONAL MATRICES 98
4.12.2 SYSTEMS WITH FIVE-DIAGONAL SYMMETRIE MATRICES 100
4.13 LINEAR SYSTEMS WITH BAND MATRICES 102
4.14 SOLVING LINEAR SYSTEMS VIA HOUSEHOLDER TRANSFORMATIONS 107 4.15
ERRORS, CONDITIONING AND ITERATIVE REFINEMENT 112
4.15.1 ERRORS AND THE CONDITION NUMBER 112
4.15.2 CONDITION ESTIMATES 114
4.15.3 IMPROVING THE CONDITION NUMBER 116
4.15.4 ITERATIVE REFINEMENT 117
4.16 SYSTEMS OF EQUATIONS WITH BLOCK MATRICES 119
4.16.1 PRELIMINARY REMARKS 119
4.16.2 GAUSS ALGORITHM FOR BLOCK MATRICES 120
4.16.3 GAUSS ALGORITHM FOR BLOCK TRIDIAGONAL SYSTEMS 121
4.16.4 OTHER BLOCK METHODS 121
4.17 THE ALGORITHM OF CUTHILL-MCKEE FOR SPARSE SYMMETRIE MATRICES 122
4.18 RECOMMENDATIONS FOR SELECTING A METHOD 127
IMAGE 5
XVI CONTENTS
5 ITERATIVE METHODS FOR LINEAR SYSTEMS 131
5.1 PRELIMINARY REMARKS 131
5.2 VECTOR AND MATRIX NORMS 132
5.3 THE JACOBI METHOD 133
5.4 THE GAUSS-SEIDEL ITERATION 137
5.5 A RELAXATION METHOD USING THE JACOBI METHOD 139
5.6 A RELAXATION METHOD USING THE GAUSS-SEIDEL METHOD 140
5.6.1 ITERATION RULE 140
5.6.2 ESTIMATE FOR THE OPTIMAL RELAXATION COEMCIENT, AN ADAPTIVE SOR
METHOD 141
6 SYSTEMS OF NONLINEAR EQUATIONS 143
6.1 GENERAL ITERATIVE METHODS 143
6.2 SPECIAL ITERATIVE METHODS 148
6.2.1 NEWTON METHODS FOR NONLINEAR SYSTEMS 148
6.2.1.1 THE BASIC NEWTON METHOD 148
6.2.1.2 DAMPED NEWTON METHOD FOR SYSTEMS 149
6.2.2 REGULA FALSI FOR NONLINEAR SYSTEMS 151
6.2.3 METHOD OF STEEPEST DESCENT FOR NONLINEAR SYSTEMS 152
6.2.4 BROWN S METHOD FOR NONLINEAR SYSTEMS 154
6.3 CHOOSING A METHOD 154
7 EIGENVALUES AND EIGENVECTORS OF MATRICES 155
7.1 BASIC CONCEPTS -. 155
7.2 DIAGONALIZABLE MATRICES AND THE CONDITIONING OF THE EIGENVALUE
PROBLEM 157
7.3 VECTOR ITERATION 159
7.3.1 THE DOMINANT EIGENVALUE AND THE ASSOCIATED EIGENVECTOR OF A MATRIX
159
7.3.2 DETERMINATION OF THE EIGENVALUE CLOSEST TO ZERO 164
7.3.3 EIGENVALUES IN BETWEEN 164
7.4 THE RAYLEIGH QUOTIENT FOR HERMITIAN MATRICES 166
7.5 THE KRYLOV METHOD 167
7.5.1 DETERMINING THE EIGENVALUES 167
7.5.2 DETERMINING THE EIGENVECTORS 169
7.6 EIGENVALUES OF POSITIVE DEFINITE TRIDIAGONAL MATRICES, THE QD
ALGORITHM 170
7.7 TRANSFORMATION TO HESSENBERG FORM, THE LR AND QR ALGORITHMS 171
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CONTENTS
XVII
7.7.1 TRANSFORMATION OF A MATRIX TO UPPER HESSENBERG FORM 172 7.7.2 THE
LR ALGORITHM 174
7.7.3 THE BASIC QR ALGORITHM 175
7.8 EIGENVALUES AND EIGENVECTORS OF A MATRIX VIA THE QR ALGORITHM 176
7.9 DECISION STRATEGY 178
8 LINEAR AND NONLINEAR APPROXIMATION 179
8.1 LINEAR APPROXIMATION 180
8.1.1 STATEMENT OF THE PROBLEM AND BEST APPROXIMATION 180
8.1.2 LINEAR CONTINUOUS ROOT-MEAN-SQUARE APPROXIMATION 184 8.1.3
DISCRETE LINEAR ROOT-MEAN-SQUARE APPROXIMATION 188
8.1.3.1 NORMAL EQUATIONS FOR DISCRETE LINEAR LEAST SQUARES 188 8.1.3.2
DISCRETE LEAST SQUARES VIA ALGEBRAIC POLYNOMIALS AND ORTHOGONAL
POLYNOMIALS 191
8.1.3.3 LINEAR REGRESSION, THE LEAST SQUARES SOLUTION USING LINEAR
ALGEBRAIC POLYNOMIALS 193
8.1.3.4 SOLVING LINEAR LEAST SQUARES PROBLEMS USING HOUSEHOLDER
TRANSFORMATIONS 194
8.1.4 APPROXIMATION OF POLYNOMIALS BY CHEBYSHEV POLYNOMIALS . 196
8.1.4.1 BEST UNIFORM APPROXIMATION 197
8.1.4.2 APPROXIMATION BY CHEBYSHEV POLYNOMIALS 198
8.1.5 APPROXIMATION OF PERIODIC FUNCTIONS AND THE FFT 204
8.1.5.1 ROOT-MEAN-SQUARE APPROXIMATION OF PERIODIC FUNCTIONS 204 8.1.5.2
TRIGONOMETRIE INTERPOLATION 205
8.1.5.3 COMPLEX DISCRETE FOURIER TRANSFORMATION (FFT) 207
8.1.6 ERROR ESTIMATES FOR LINEAR APPROXIMATION 209
8.1.6.1 ESTIMATES FOR THE ERROR IN BEST APPROXIMATION 209
8.1.6.2 ERROR ESTIMATES FOR SIMULTANEOUS APPROXIMATION OF A FUNCTION AND
ITS DERIVATIVES 211
8.1.6.3 APPROXIMATION ERROR ESTIMATES USING LINEAR PROJECTION OPERATORS
213
8.2 NONLINEAR APPROXIMATION 215
8.2.1 TRANSFORMATION METHOD FOR NONLINEAR LEAST SQUARES 215
8.2.2 NONLINEAR ROOT-MEAN-SQUARE FITTING 217
8.3 DECISION STRATEGY 218
H
IMAGE 7
CONTENTS
9 POLYNOMIAL AND RATIONAL INTERPOLATION 219
9.1 THE PROBLEM 219
9.2 LAGRANGE INTERPOLATION FORMULA 221
9.2.1 LAGRANGE FORMULA FOR ARBITRARY NODES 221
9.2.2 LAGRANGE FORMULA FOR EQUIDISTANT NODES 222
9.3 THE AITKEN INTERPOLATION SCHEME FOR ARBITRARY NODES 223
9.4 INVERSE INTERPOLATION ACCORDING TO AITKEN 225
9.5 NEWTON INTERPOLATION FORMULA 226
9.5.1 NEWTON FORMULA FOR ARBITRARY NODES 226
9.5.2 NEWTON FORMULA FOR EQUIDISTANT NODES 227
9.6 REMAINDER OF AN INTERPOLATION AND ESTIMATES OF THE INTERPOLATION
ERROR 229
9.7 RATIONAL INTERPOLATION 235
9.8 INTERPOLATION FOR FUNCTIONS IN SEVERAL VARIABLES 239
9.8.1 LAGRANGE INTERPOLATION FORMULA FOR TWO VARIABLES 239
9.8.2 SHEPARD INTERPOLATION 241
9.9 HINTS FOR SELECTING AN APPROPRIATE INTERPOLATION METHOD 247
10 INTERPOLATING POLYNOMIAL SPLINES FOR CONSTRUCTING SMOOTH CURVES 251
10.1 CUBIC POLYNOMIAL SPLINES 251
10.1.1 DEFINITION OF INTERPOLATING CUBIC SPLINE FUNCTIONS 252
10.1.2 COMPUTATION OF NON-PARAMETRIC CUBIC SPLINES 254
10.1.3 COMPUTING PARAMETRIC CUBIC SPLINES 259
10.1.4 JOINED INTERPOLATING POLYNOMIAL SPLINES 266
10.1.5 CONVERGENCE AND ERROR ESTIMATES FOR INTERPOLATING CUBIC SPLINES
272
10.2 HERMITE SPLINES OF FIFTH DEGREE 275
10.2.1 DEFINITION OF HERMITE SPLINES 275
10.2.2 COMPUTATION OF NON-PARAMETRIC HERMITE SPLINES 276
10.2.3 COMPUTATION OF PARAMETRIC HERMITE SPLINES 280
10.3 HINTS FOR SELECTING APPROPRIATE INTERPOLATING OR APPROXIMATING
SPLINES 282
11 CUBIC FITTING SPLINES FOR CONSTRUCTING SMOOTH CURVES . .. 287
11.1 THE PROBLEM 287
11.2 DEFINITION OF FITTING SPLINE FUNCTIONS 288
11.3 NON-PARAMETRIC CUBIC FITTING SPLINES 289
IMAGE 8
XIX
11.4 PARAMETRIC CUBIC FITTING SPLINES 296
11.5 DECISION STRATEGY 297
12 TWO-DIMENSIONAL SPLINES, SURFACE SPLINES, BEZIER SPLINES, B-SPLINES
299
12.1 INTERPOLATING TWO-DIMENSIONAL CUBIC SPLINES FOR CONSTRUCTING SMOOTH
SURFACES 299
12.2 TWO-DIMENSIONAL INTERPOLATING SURFACE SPLINES 309
12.3 BEZIER SPLINES 313
12.3.1 BEZIER SPLINE CURVES 313
12.3.2 BEZIER SPLINE SURFACES 316
12.3.3 MODIFIED INTERPOLATING CUBIC BEZIER SPLINES 324
12.4 B-SPLINES 325
12.4.1 B-SPLINE-CURVES 325
12.4.2 B-SPLINE-SURFACES 331
12.5 HINTS 335
13 AKIMA AND RENNER SUBSPLINES 341
13.1 AKIMA SUBSPLINES 341
13.2 RENNER SUBSPLINES 344
13.3 ROUNDING OF CORNERS WITH AKIMA AND RENNER SPLINES 347
13.4 APPROXIMATE COMPUTATION OF ARE LENGTH 349
13.5 SELECTION HINTS 350
14 NUMERICAL DIFFERENTIATION 353
14.1 THE TASK 353
14.2 DIFFERENTIATION USING INTERPOLATING POLYNOMIALS 354
14.3 DIFFERENTIATION VIA INTERPOLATING CUBIC SPLINES 358
14.4 DIFFERENTIATION BY THE ROMBERG METHOD 358
14.5 DECISION HINTS 360
15 NUMERICAL INTEGRATION 361
15.1 PRELIMINARY REMARKS 361
15.2 INTERPOLATING QUADRATURE FORMULAS 364
15.3 NEWTON-COTES FORMULAS 366
15.3.1 THE TRAPEZOIDAL RULE 367
15.3.2 SIMPSON S RULE 370
IMAGE 9
CONTENTS
15.3.3 THE 3/8 FORMULA 371
15.3.4 OTHER NEWTON-COTES FORMULAS 373
15.3.5 THE ERROR ORDER OF NEWTON-COTES FORMULAS 375
15.4 MACLAURIN QUADRATURE FORMULAS 376
15.4.1 THE TANGENT TRAPEZOIDAL FORMULA 376
15.4.2 OTHER MACLAURIN FORMULAS 378
15.5 EULER-MACLAURIN FORMULAS 380
15.6 CHEBYSHEV QUADRATURE FORMULAS 382
15.7 GAUSS QUADRATURE FORMULAS 385
15.8 CALCULATION OF WEIGHTS AND NODES OF GENERALIZED GAUSSIAN QUADRATURE
FORMULAS 389
15.9 CLENSHAW-CURTIS QUADRATURE FORMULAS 392
15.10 ROMBERG INTEGRATION 394
15.11 ERROR ESTIMATES AND COMPUTATIONAL ERRORS 397
15.12 ADAPTIVE QUADRATURE METHODS 400
15.13 CONVERGENCE OF QUADRATURE FORMULAS 400
15.14 HINTS FOR CHOOSING AN APPROPRIATE METHOD 401
16 NUMERICAL CUBATURE 403
16.1 THE PROBLEM 403
16.2 INTERPOLATING CUBATURE FORMULAS 406
16.3 NEWTON-COTES CUBATURE FORMULAS FOR RECTANGULAR REGIONS 408 16.4
NEWTON-COTES CUBATURE FORMULAS FOR TRIANGLES 413
16.5 ROMBERG CUBATURE FOR RECTANGULAR REGIONS 414
16.6 GAUSS CUBATURE FORMULAS FOR RECTANGLES 417
16.7 GAUSS CUBATURE FORMULAS FOR TRIANGLES 419
16.7.1 RIGHT TRIANGLES WITH LEGS PARALLEL TO THE AXIS 419
16.7.2 GENERAL TRIANGLES 420
16.8 RIEMANN DOUBLE INTEGRALS USING BICUBIC SPLINES 421
16.9 DECISION STRATEGY 422
17 INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS 423
17.1 THE PROBLEM 423
17.2 PRINCIPLES OF THE NUMERICAL METHODS 424
17.3 ONE-STEP METHODS 426
17.3.1 THE EULER-CAUCHY POLYGONAL METHOD 426
17.3.2 THE IMPROVED EULER-CAUCHY METHOD 427
IMAGE 10
CONTENTS XXI
17.3.3 THE PREDICTOR-CORRECTOR METHOD OF HEUN 428
17.3.4 EXPLICIT RUNGE-KUTTA METHODS 430
17.3.4.1 CONSTRUCTION OF RUNGE-KUTTA METHODS 430
17.3.4.2 THE CLASSICAL RUNGE-KUTTA METHOD 430
17.3.4.3 A LIST OF EXPLICIT RUNGE-KUTTA FORMULAS 432
17.3.4.4 EMBEDDING FORMULAS 436
17.3.5 IMPLICIT RUNGE-KUTTA METHODS OF GAUSSIAN TYPE 449
17.3.6 CONSISTENCE AND CONVERGENCE OF ONE-STEP METHODS 451
17.3.7 ERROR ESTIMATION AND STEP SIZE CONTROL 452
17.3.7.1 ERROR ESTIMATION 452
17.3.7.2 AUTOMATIC STEP SIZE CONTROL, ADAPTIVE METHODS FOR INITIAL VALUE
PROBLEMS 454
17.4 MULTI-STEP METHODS 457
17.4.1 THE PRINCIPLE OF MULTI-STEP METHODS 457
17.4.2 THE ADAMS-BASHFORTH METHOD 458
17.4.3 THE PREDICTOR-CORRECTOR METHOD OF ADAMS-MOULTON 460
17.4.4 THE ADAMS-STOERMER METHOD 465
17.4.5 ERROR ESTIMATES FOR MULTI-STEP METHODS 466
17.4.6 COMPUTATIONAL ERROR OF ONE-STEP AND MULTI-STEP METHODS 467 17.5
BULIRSCH-STOER-GRAGG EXTRAPOLATION 468
17.6 STABILITY 471
17.6.1 PRELIMINARY REMARKS 471
17.6.2 STABILITY OF DIFFERENTIAL EQUATIONS 472
17.6.3 STABILITY OF THE NUMERICAL METHOD 473
17.7 STIFF SYSTEMS OF DIFFERENTIAL EQUATIONS 477
17.7.1 THE PROBLEM 477
17.7.2 CRITERIA FOR THE STIFFNESS OF A SYSTEM 478
17.7.3 GEAR S METHOD FOR INTEGRATING STIFF SYSTEMS .479
17.8 SUGGESTIONS FOR CHOOSING AMONG THE METHODS 484
18 BOUNDARY VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS 489
18.1 STATEMENT OF THE PROBLEM 489
18.2 REDUCTION OF BOUNDARY VALUE PROBLEMS TO INITIAL VALUE PROBLEMS 490
18.2.1 BOUNDARY VALUE PROBLEMS FOR NONLINEAR DIFFERENTIAL EQUATIONS OF
SECOND ORDER 490
18.2.2 BOUNDARY VALUE PROBLEMS FOR SYSTEMS OF DIFFERENTIAL EQUATIONS OF
FIRST ORDER 492
IMAGE 11
XXII CONTENTS
18.2.3 THE MULTIPLE SHOOTING METHOD 494
18.3 DIFFERENCE METHODS 497
18.3.1 THE ORDINARY DIFFERENCE METHOD 497
18.3.2 HIGHER ORDER DIFFERENCE METHODS 504
18.3.3 ITERATIVE SOLUTION OF LINEAR SYSTEMS FOR SPECIAL BOUNDARY VALUE
PROBLEMS 506
18.3.4 LINEAR EIGENVALUE PROBLEMS 507
A APPENDIX: STANDARD F O R T R AN 77 SUBROUTINES 509
A.L PREFACE OF THE APPENDIX 511
A.2 INFORMATION ON CAMPUS AND SITE LICENSES, AS WELL AS ON OTHER
SOFTWARE PACKAGES 513
A.3 CONTENTS OF THE ENCLOSED CD 516
CONTENTS OF THE APPENDIX 517
A.4 FORTRAN 77 SUBROUTINES 521
B BIBLIOGRAPHY 575
LITERATURE FOR OTHER TOPICS 593
- NUMERICAL TREATMENT OF PARTIAL DIFFERENTIAL EQUATIONS 593
- FINITE ELEMENT METHOD 594
C INDEX 597
|
| any_adam_object | 1 |
| author | Engeln-Müllges, Gisela 1940- Uhlig, Frank |
| author_GND | (DE-588)110051203 |
| author_facet | Engeln-Müllges, Gisela 1940- Uhlig, Frank |
| author_role | aut aut |
| author_sort | Engeln-Müllges, Gisela 1940- |
| author_variant | g e m gem f u fu |
| building | Verbundindex |
| bvnumber | BV010982517 |
| callnumber-first | Q - Science |
| callnumber-label | QA297 |
| callnumber-raw | QA297 |
| callnumber-search | QA297 |
| callnumber-sort | QA 3297 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 900 ST 250 ST 600 |
| classification_tum | DAT 532f MAT 650f DAT 360f |
| ctrlnum | (OCoLC)35121756 (DE-599)BVBBV010982517 |
| dewey-full | 519.4/0285/5133 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.4/0285/5133 |
| dewey-search | 519.4/0285/5133 |
| dewey-sort | 3519.4 3285 45133 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| genre | 1\p (DE-588)4155008-0 Formelsammlung gnd-content |
| genre_facet | Formelsammlung |
| id | DE-604.BV010982517 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:04:17Z |
| institution | BVB |
| isbn | 3540605290 |
| language | English German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007349443 |
| oclc_num | 35121756 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-20 DE-355 DE-BY-UBR DE-703 DE-29T DE-19 DE-BY-UBM DE-706 DE-11 |
| owner_facet | DE-91G DE-BY-TUM DE-20 DE-355 DE-BY-UBR DE-703 DE-29T DE-19 DE-BY-UBM DE-706 DE-11 |
| physical | XXII, 602 S. graph. Darst. 1 CD-ROM (12 cm) |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer |
| record_format | marc |
| spellingShingle | Engeln-Müllges, Gisela 1940- Uhlig, Frank Numerical algorithms with Fortran FORTRAN 77 (Computer program language) Numerical analysis Numerical analysis Computer programs Programm (DE-588)4047394-6 gnd C Programmiersprache (DE-588)4113195-2 gnd FORTRAN (DE-588)4017984-9 gnd Algorithmus (DE-588)4001183-5 gnd Numerisches Verfahren (DE-588)4128130-5 gnd TURBO-PASCAL (DE-588)4117264-4 gnd ANSI C (DE-588)4233557-7 gnd Numerische Mathematik (DE-588)4042805-9 gnd FORTRAN 77 (DE-588)4113601-9 gnd FORTRAN 90 (DE-588)4267480-3 gnd |
| subject_GND | (DE-588)4047394-6 (DE-588)4113195-2 (DE-588)4017984-9 (DE-588)4001183-5 (DE-588)4128130-5 (DE-588)4117264-4 (DE-588)4233557-7 (DE-588)4042805-9 (DE-588)4113601-9 (DE-588)4267480-3 (DE-588)4155008-0 |
| title | Numerical algorithms with Fortran |
| title_alt | Numerik-Algorithmen mit FORTRAN-77-Programmen |
| title_auth | Numerical algorithms with Fortran |
| title_exact_search | Numerical algorithms with Fortran |
| title_full | Numerical algorithms with Fortran Gisela Engeln-Müllges ; Frank Uhlig |
| title_fullStr | Numerical algorithms with Fortran Gisela Engeln-Müllges ; Frank Uhlig |
| title_full_unstemmed | Numerical algorithms with Fortran Gisela Engeln-Müllges ; Frank Uhlig |
| title_short | Numerical algorithms with Fortran |
| title_sort | numerical algorithms with fortran |
| topic | FORTRAN 77 (Computer program language) Numerical analysis Numerical analysis Computer programs Programm (DE-588)4047394-6 gnd C Programmiersprache (DE-588)4113195-2 gnd FORTRAN (DE-588)4017984-9 gnd Algorithmus (DE-588)4001183-5 gnd Numerisches Verfahren (DE-588)4128130-5 gnd TURBO-PASCAL (DE-588)4117264-4 gnd ANSI C (DE-588)4233557-7 gnd Numerische Mathematik (DE-588)4042805-9 gnd FORTRAN 77 (DE-588)4113601-9 gnd FORTRAN 90 (DE-588)4267480-3 gnd |
| topic_facet | FORTRAN 77 (Computer program language) Numerical analysis Numerical analysis Computer programs Programm C Programmiersprache FORTRAN Algorithmus Numerisches Verfahren TURBO-PASCAL ANSI C Numerische Mathematik FORTRAN 77 FORTRAN 90 Formelsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007349443&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT engelnmullgesgisela numerikalgorithmenmitfortran77programmen AT uhligfrank numerikalgorithmenmitfortran77programmen AT engelnmullgesgisela numericalalgorithmswithfortran AT uhligfrank numericalalgorithmswithfortran |
Inhaltsverzeichnis
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Paper/Kapitel scannen lassen
Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 DAT 532f 2001 A 13379 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |
Teilbibliothek Maschinenwesen
| Signatur: |
0702 DAT 532f 97 A 70036 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |