Scientific computing with MATLAB and Octave:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2014
|
| Ausgabe: | 4. ed. |
| Schriftenreihe: | Texts in computational science and engineering
2 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XVIII, 442 S. graph. Darst. |
| ISBN: | 9783642453663 |
Internformat
MARC
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| 100 | 1 | |a Quarteroni, Alfio |d 1952- |e Verfasser |0 (DE-588)120370158 |4 aut | |
| 245 | 1 | 0 | |a Scientific computing with MATLAB and Octave |c Alfio Quarteroni ; Fausto Saleri ; Paola Gervasio |
| 250 | |a 4. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2014 | |
| 300 | |a XVIII, 442 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
| _version_ | 1806326731013881856 |
|---|---|
| adam_text |
1 WHAT CAN'T BE IGNORED 1
1.1 THE MATLAB AND OCTAVE ENVIRONMENTS 1
1.2 REAL NUMBERS 3
1.2.1 HOW WE REPRESENT THEM 3
1.2.2 HOW WE OPERATE WITH FLOATING-POINT NUMBERS 6
1.3 COMPLEX NUMBERS 8
1.4 MATRICES 10
1.4.1 VECTORS 14
1.5 REAL FUNCTIONS 16
1.5.1 THE ZEROS 19
1.5.2 POLYNOMIALS 20
1.5.3 INTEGRATION AND DIFFERENTIATION 22
1.6 TO ERR IS NOT ONLY HUMAN 25
1.6.1 TALKING ABOUT COSTS 28
1.7 THE MATLAB LANGUAGE 30
1.7.1 MATLAB STATEMENTS 32
1.7.2 PROGRAMMING IN MATLAB *. 34
1.7.3 EXAMPLES OF DIFFERENCES BETWEEN MATLAB
AND OCTAVE LANGUAGES 38
1.8 WHAT WE HAVEN'T TOLD YOU 38
1.9 EXERCISES 39
2 NONLINEAR EQUATIONS 41
2.1 SOME REPRESENTATIVE PROBLEMS 41
2.2 THE BISECTION METHOD 43
2.3 THE NEWTON METHOD 47
2.3.1 HOW TO TERMINATE NEWTON'S ITERATIONS 50
2.4 THE SECANT METHOD 51
2.5 SYSTEMS OF NONLINEAR EQUATIONS 52
XI
HTTP://D-NB.INFO/1044795212
XII CONTENTS
2.6 FIXED POINT ITERATIONS 56
2.6.1 HOW TO TERMINATE FIXED POINT ITERATIONS 62
2.7 ACCELERATION USING AITKEN METHOD 63
2.8 ALGEBRAIC POLYNOMIALS 67
2.8.1 HORNER'S ALGORITHM 68
2.8.2 THE NEWTON-HORNER METHOD 70
2.9 WHAT WE HAVEN'T TOLD YOU 72
2.10 EXERCISES 74
3 APPROXIMATION OF FUNCTIONS AND DATA 77
3.1 SOME REPRESENTATIVE PROBLEMS 77
3.2 APPROXIMATION BY TAYLOR'S POLYNOMIALS 79
3.3 INTERPOLATION 80
3.3.1 LAGRANGIAN POLYNOMIAL INTERPOLATION 81
3.3.2 STABILITY OF POLYNOMIAL INTERPOLATION 86
3.3.3 INTERPOLATION AT CHEBYSHEV NODES 87
3.3.4 BARYCENTRIC INTERPOLATION FORMULA 90
3.3.5 TRIGONOMETRIC INTERPOLATION AND FFT 93
3.4 PIECEWISE LINEAR INTERPOLATION 98
3.5 APPROXIMATION BY SPLINE FUNCTIONS 100
3.6 THE LEAST-SQUARES METHOD 104
3.7 WHAT WE HAVEN'T TOLD YOU 108
3.8 EXERCISES 110
4 NUMERICAL DIFFERENTIATION AND INTEGRATION 113
4.1 SOME REPRESENTATIVE PROBLEMS 113
4.2 APPROXIMATION OF FUNCTION DERIVATIVES 115
4.3 NUMERICAL INTEGRATION 117
4.3.1 MIDPOINT FORMULA 118
4.3.2 TRAPEZOIDAL FORMULA 120
4.3.3 SIMPSON FORMULA 121
4.4 INTERPOLATORY QUADRATURES 123
4.5 SIMPSON ADAPTIVE FORMULA 127
4.6 MONTE CARLO METHODS FOR NUMERICAL INTEGRATION 131
4.7 WHAT WE HAVEN'T TOLD YOU 133
4.8 EXERCISES 134
5 LINEAR SYSTEMS 137
5.1 SOME REPRESENTATIVE PROBLEMS 137
5.2 LINEAR SYSTEM AND COMPLEXITY 142
5.3 THE LU FACTORIZATION METHOD 143
5.4 THE PIVOTING TECHNIQUE 154
5.4.1 THE
FILL-IN
OF A MATRIX 157
5.5 HOW ACCURATE IS THE SOLUTION OF A LINEAR SYSTEM? 158
5.6 HOW TO SOLVE A TRIDIAGONAL SYSTEM 162
CONTENTS XIII
5.7 OVERDETERMINED SYSTEMS 163
5.8 WHAT IS HIDDEN BEHIND THE MATLAB COMMAND \ 166
5.9 ITERATIVE METHODS 168
5.9.1 HOW TO CONSTRUCT AN ITERATIVE METHOD 169
5.10 RICHARDSON AND GRADIENT METHODS 174
5.11 THE CONJUGATE GRADIENT METHOD 177
5.12 WHEN SHOULD AN ITERATIVE METHOD BE STOPPED? 180
5.13 TO WRAP-UP: DIRECT OR ITERATIVE? 182
5.14 WHAT WE HAVEN'T TOLD YOU 188
5.15 EXERCISES 188
6 EIGENVALUES AND EIGENVECTORS 193
6.1 SOME REPRESENTATIVE PROBLEMS 194
6.2 THE POWER METHOD 196
6.2.1 CONVERGENCE ANALYSIS 199
6.3 GENERALIZATION OF THE POWER METHOD 201
6.4 HOW TO COMPUTE THE SHIFT 203
6.5 COMPUTATION OF ALL THE EIGENVALUES 206
6.6 WHAT WE HAVEN'T TOLD YOU 209
6.7 EXERCISES 210
7 NUMERICAL OPTIMIZATION 213
7.1 SOME REPRESENTATIVE PROBLEMS 214
7.2 UNCONSTRAINED OPTIMIZATION 217
7.3 DERIVATIVE FREE METHODS 219
7.3.1 GOLDEN SECTION AND QUADRATIC INTERPOLATION
METHODS 219
7.3.2 NELDER AND MEAD METHOD 223
7.4 THE NEWTON METHOD 227
7.5 DESCENT (OR LINE SEARCH) METHODS 228
7.5.1 DESCENT DIRECTIONS 229
7.5.2 STRATEGIES FOR CHOOSING THE STEPLENGTH AK 231
7.5.3 THE DESCENT METHOD WITH NEWTON'S DIRECTIONS 237
7.5.4 DESCENT METHODS WITH QUASI-NEWTON DIRECTIONS . 238
7.5.5 GRADIENT AND CONJUGATE GRADIENT
DESCENT METHODS 240
7.6 TRUST REGION METHODS 242
7.7 THE NONLINEAR LEAST SQUARES METHOD 248
7.7.1 GAUSS-NEWTON METHOD 249
7.7.2 LEVENBERG-MARQUARDT'S METHOD 252
7.8 CONSTRAINED OPTIMIZATION 253
7.8.1 THE PENALTY METHOD 259
7.8.2 THE AUGMENTED LAGRANGIAN METHOD 264
7.9 WHAT WE HAVEN'T TOLD YOU 267
7.10 EXERCISES 268
XIV CONTENTS
8 ORDINARY DIFFERENTIAL EQUATIONS 271
8.1 SOME REPRESENTATIVE PROBLEMS 271
8.2 THE CAUCHY PROBLEM 274
8.3 EULER METHODS 275
8.3.1 CONVERGENCE ANALYSIS 278
8.4 THE CRANK-NICOLSON METHOD 282
8.5 ZERO-STABILITY 284
8.6 STABILITY ON UNBOUNDED INTERVALS 286
8.6.1 THE REGION OF ABSOLUTE STABILITY 289
8.6.2 ABSOLUTE STABILITY CONTROLS PERTURBATIONS 290
8.6.3 STEPSIZE ADAPTIVITY FOR THE FORWARD EULER
METHOD 297
8.7 HIGH ORDER METHODS 300
8.8 THE PREDICTOR-CORRECTOR METHODS 305
8.9 SYSTEMS OF DIFFERENTIAL EQUATIONS 307
8.10 SOME EXAMPLES 313
8.10.1 THE SPHERICAL PENDULUM 313
8.10.2 THE THREE-BODY PROBLEM 317
8.10.3 SOME STIFF PROBLEMS 319
8.11 WHAT WE HAVEN'T TOLD YOU 325
8.12 EXERCISES 326
9 NUMERICAL APPROXIMATION OF BOUNDARY-VALUE
PROBLEMS 329
9.1 SOME REPRESENTATIVE PROBLEMS 330
9.2 APPROXIMATION OF BOUNDARY-VALUE PROBLEMS 332
9.2.1 FINITE DIFFERENCE APPROXIMATION OF THE
ONE-DIMENSIONAL POISSON PROBLEM 333
9.2.2 FINITE DIFFERENCE APPROXIMATION OF A
CONVECTION-DOMINATED PROBLEM 336
9.2.3 FINITE ELEMENT APPROXIMATION OF THE
ONE-DIMENSIONAL POISSON PROBLEM 337
9.2.4 FINITE DIFFERENCE APPROXIMATION OF THE
TWO-DIMENSIONAL POISSON PROBLEM 341
9.2.5 CONSISTENCY AND CONVERGENCE OF FINITE DIFFERENCE
DISCRETIZATION OF THE POISSON PROBLEM 347
9.2.6 FINITE DIFFERENCE APPROXIMATION OF THE
ONE-DIMENSIONAL HEAT EQUATION 348
9.2.7 FINITE ELEMENT APPROXIMATION OF THE
ONE-DIMENSIONAL HEAT EQUATION 352
9.3 HYPERBOLIC EQUATIONS: A SCALAR PURE ADVECTION
PROBLEM 355
9.3.1 FINITE DIFFERENCE DISCRETIZATION OF THE SCALAR
TRANSPORT EQUATION 357
CONTENTS
XV
9.3.2 FINITE DIFFERENCE ANALYSIS FOR THE SCALAR TRANSPORT
EQUATION 359
9.3.3 FINITE ELEMENT SPACE DISCRETIZATION OF THE SCALAR
ADVECTION EQUATION 366
9.4 THE WAVE EQUATION 367
9.4.1 FINITE DIFFERENCE APPROXIMATION OF THE WAVE
EQUATION 369
9.5 WHAT WE HAVEN'T TOLD YOU 373
9.6 EXERCISES 374
10 SOLUTIONS OF THE EXERCISES 377
10.1 CHAPTER 1 377
10.2 CHAPTER 2 380
10.3 CHAPTER 3 385
10.4 CHAPTER 4 389
10.5 CHAPTER 5 394
10.6 CHAPTER 6 401
10.7 CHAPTER 7 404
10.8 CHAPTER 8 411
10.9 CHAPTER 9 422
REFERENCES 429
INDEX 435 |
| any_adam_object | 1 |
| author | Quarteroni, Alfio 1952- Saleri, Fausto 1965-2007 Gervasio, Paola |
| author_GND | (DE-588)120370158 (DE-588)120434571 |
| author_facet | Quarteroni, Alfio 1952- Saleri, Fausto 1965-2007 Gervasio, Paola |
| author_role | aut aut aut |
| author_sort | Quarteroni, Alfio 1952- |
| author_variant | a q aq f s fs p g pg |
| building | Verbundindex |
| bvnumber | BV041551808 |
| classification_rvk | ST 601 |
| classification_tum | DAT 306f MAT 650f |
| ctrlnum | (OCoLC)865147291 (DE-599)DNB1044795212 |
| dewey-full | 518 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518 |
| dewey-search | 518 |
| dewey-sort | 3518 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| edition | 4. ed. |
| format | Book |
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| id | DE-604.BV041551808 |
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| indexdate | 2024-08-03T01:10:10Z |
| institution | BVB |
| isbn | 9783642453663 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026997532 |
| oclc_num | 865147291 |
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| owner_facet | DE-91G DE-BY-TUM DE-11 DE-29T DE-573 DE-384 DE-92 DE-1102 DE-188 DE-83 |
| physical | XVIII, 442 S. graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Springer |
| record_format | marc |
| series | Texts in computational science and engineering |
| series2 | Texts in computational science and engineering |
| spelling | Quarteroni, Alfio 1952- Verfasser (DE-588)120370158 aut Scientific computing with MATLAB and Octave Alfio Quarteroni ; Fausto Saleri ; Paola Gervasio 4. ed. Berlin [u.a.] Springer 2014 XVIII, 442 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in computational science and engineering 2 Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf MATLAB (DE-588)4329066-8 gnd rswk-swf Wissenschaftliches Rechnen (DE-588)4338507-2 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 s MATLAB (DE-588)4329066-8 s DE-604 Wissenschaftliches Rechnen (DE-588)4338507-2 s 1\p DE-604 Saleri, Fausto 1965-2007 Verfasser (DE-588)120434571 aut Gervasio, Paola Verfasser aut Erscheint auch als Online-Ausgabe 978-3-642-45367-0 Texts in computational science and engineering 2 (DE-604)BV016971315 2 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4528688&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026997532&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Quarteroni, Alfio 1952- Saleri, Fausto 1965-2007 Gervasio, Paola Scientific computing with MATLAB and Octave Texts in computational science and engineering Numerische Mathematik (DE-588)4042805-9 gnd MATLAB (DE-588)4329066-8 gnd Wissenschaftliches Rechnen (DE-588)4338507-2 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4329066-8 (DE-588)4338507-2 |
| title | Scientific computing with MATLAB and Octave |
| title_auth | Scientific computing with MATLAB and Octave |
| title_exact_search | Scientific computing with MATLAB and Octave |
| title_full | Scientific computing with MATLAB and Octave Alfio Quarteroni ; Fausto Saleri ; Paola Gervasio |
| title_fullStr | Scientific computing with MATLAB and Octave Alfio Quarteroni ; Fausto Saleri ; Paola Gervasio |
| title_full_unstemmed | Scientific computing with MATLAB and Octave Alfio Quarteroni ; Fausto Saleri ; Paola Gervasio |
| title_short | Scientific computing with MATLAB and Octave |
| title_sort | scientific computing with matlab and octave |
| topic | Numerische Mathematik (DE-588)4042805-9 gnd MATLAB (DE-588)4329066-8 gnd Wissenschaftliches Rechnen (DE-588)4338507-2 gnd |
| topic_facet | Numerische Mathematik MATLAB Wissenschaftliches Rechnen |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4528688&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026997532&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV016971315 |
| work_keys_str_mv | AT quarteronialfio scientificcomputingwithmatlabandoctave AT salerifausto scientificcomputingwithmatlabandoctave AT gervasiopaola scientificcomputingwithmatlabandoctave |