Scientific computing with MATLAB and Octave: with 12 tables
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English Italian |
| Published: |
Berlin [u.a.]
Springer
2006
|
| Edition: | 2. ed. |
| Series: | Texts in computational science and engineering
2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 307 - 310 |
| Physical Description: | XVI, 318 S. graph. Darst. |
| ISBN: | 9783540326120 354032612X |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804135748847271936 |
|---|---|
| adam_text | ALFIO QUARTERONI FAUSTO SALERI SCIENTIFIC COMPUTING WITH MATLAB AND
OCTAVE SECOND EDITION WITH 108 FIGURES AND 12 TABLES SPRINGER CONTENTS 1
WHAT CAN T BE IGNORED 1 1.1 REAL NUMBERS 2 1.1.1 HOW WE REPRESENT THEM 2
1.1.2 HOW WE OPERATE WITH FLOATING-POINT NUMBERS 4 1.2 COMPLEX NUMBERS 6
1.3 MATRICES 8 1.3.1 VECTORS 14 1.4 REAL FUNCTIONS 15 1.4.1 THE ZEROS 16
1.4.2 POLYNOMIALS 18 1.4.3 INTEGRATION AND DIFFERENTIATION 21 1.5 TO ERR
IS NOT ONLY HUMAN 23 1.5.1 TALKING ABOUT COSTS 26 1.6 THE MATLAB AND
OCTAVE ENVIRONMENTS 28 1.7 THE MATLAB LANGUAGE 29 1.7.1 MATLAB
STATEMENTS 31 1.7.2 PROGRAMMING IN MATLAB 32 1.7.3 EXAMPLES OF
DIFFERENCES BETWEEN MATLAB AND OCTAVE LANGUAGES 36 1.8 WHAT WE HAVEN T
TOLD YOU 37 1.9 EXERCISES 37 2 NONLINEAR EQUATIONS 39 2.1 THE BISECTION
METHOD 41 2.2 THE NEWTON METHOD 45 2.2.1 HOW TO TERMINATE NEWTON S
ITERATIONS 47 2.2.2 THE NEWTON METHOD FOR SYSTEMS OF NONLINEAR EQUATIONS
49 2.3 FIXED POINT ITERATIONS 51 2.3.1 HOW TO TERMINATE FIXED POINT
ITERATIONS 55 XII CONTENTS 2.4 ACCELERATION USING AITKEN METHOD 56 2.5
ALGEBRAIC POLYNOMIALS 60 2.5.1 HOERNER S ALGORITHM 61 2.5.2 THE
NEWTON-HOERNER METHOD 63 2.6 WHAT WE HAVEN T TOLD YOU 65 2.7 EXERCISES 67
3 APPROXIMATION OF FUNCTIONS AND DATA 71 3.1 INTERPOLATION 74 3.1.1
LAGRANGIAN POLYNOMIAL INTERPOLATION 75 3.1.2 CHEBYSHEV INTERPOLATION 80
3.1.3 TRIGONOMETRIE INTERPOLATION AND FFT 81 3.2 PIECEWISE LINEAR
INTERPOLATION 86 3.3 APPROXIMATION BY SPLINE FUNCTIONS 88 3.4 THE
LEAST-SQUARES METHOD 92 3.5 WHAT WE HAVEN T TOLD YOU 97 3.6 EXERCISES 98
4 NUMERICAL DIFFERENTIATION AND INTEGRATION 101 4.1 APPROXIMATION OF
FUNETION DERIVATIVES 103 4.2 NUMERICAL INTEGRATION 105 4.2.1 MIDPOINT
FORMULA 106 4.2.2 TRAPEZOIDAL FORMULA 108 4.2.3 SIMPSON FORMULA 109 4.3
INTERPOLATORY QUADRATURES 111 4.4 SIMPSON ADAPTIVE FORMULA 115 4.5 WHAT
WE HAVEN T TOLD YOU 119 4.6 EXERCISES 120 5 LINEAR SYSTEMS 123 5.1 THE
LU FACTORIZATION METHOD 126 5.2 THE PIVOTING TECHNIQUE 134 5.3 HOW
AECURATE IS THE LU FACTORIZATION? 136 5.4 HOW TO SOLVE A TRIDIAGONAL
SYSTEM 140 5.5 OVERDETERMINED SYSTEMS 141 5.6 WHAT IS HIDDEN BEHIND THE
COMMAND 143 5.7 ITERATIVE METHODS 144 5.7.1 HOW TO CONSTRUET AN
ITERATIVE METHOD 146 5.8 RICHARDSON AND GRADIENT METHODS 150 5.9 THE
CONJUGATE GRADIENT METHOD 153 5.10 WHEN SHOULD AN ITERATIVE METHOD BE
STOPPED? 156 5.11 TO WRAP-UP: DIRECT OR ITERATIVE? 159 5.12 WHAT WE
HAVEN T TOLD YOU 164 5.13 EXERCISES 164 CONTENTS XIII EIGENVALUES AND
EIGENVECTORS 167 6.1 THE POWER METHOD 170 6.1.1 CONVERGENCE ANALYSIS 173
6.2 GENERALIZATION OF THE POWER METHOD 174 6.3 HOW TO COMPUTE THE SHIFT
176 6.4 COMPUTATION OF ALL THE EIGENVALUES 179 6.5 WHAT WE HAVEN T TOLD
YOU 183 6.6 EXERCISES 183 ORDINARY DIFFERENTIAL EQUATIONS 187 7.1 THE
CAUCHY PROBLEM 190 7.2 EULER METHODS 191 7.2.1 CONVERGENCE ANALYSIS 194
7.3 THE CRANK-NICOLSON METHOD 197 7.4 ZERO-STABILITY 199 7.5 STABILITY
ON UNBOUNDED INTERVALS 202 7.5.1 THE REGION OF ABSOLUTE STABILITY 204
7.5.2 ABSOLUTE STABILITY CONTROLS PERTURBATIONS 205 7.6 HIGH ORDER
METHODS 212 7.7 THE PREDICTOR-CORRECTOR METHODS 216 7.8 SYSTEMS OF
DIFFERENTIAL EQUATIONS 219 7.9 SOME EXAMPLES 225 7.9.1 THE SPHERICAL
PENDULUM 225 7.9.2 THE THREE-BODY PROBLEM 228 7.9.3 SOME STIFF PROBLEMS
230 7.10 WHAT WE HAVEN T TOLD YOU 234 7.11 EXERCISES 234 NUMERICAL
METHODS FOR (INITIAL-)BOUNDARY-VALUE PROBLEMS 237 8.1 APPROXIMATION OF
BOUNDARY-VALUE PROBLEMS 240 8.1.1 APPROXIMATION BY FINITE DIFFERENCES
241 8.1.2 APPROXIMATION BY FINITE ELEMENTS 243 8.1.3 APPROXIMATION BY
FINITE DIFFERENCES OF TWO-DIMENSIONAL PROBLEMS 245 8.1.4 CONSISTENCY AND
CONVERGENCE 251 8.2 FINITE DIFFERENCE APPROXIMATION OF THE HEAT EQUATION
.... 253 8.3 THE WAVE EQUATION 257 8.3.1 APPROXIMATION BY FINITE
DIFFERENCES 260 8.4 WHAT WE HAVEN T TOLD YOU 263 8.5 EXERCISES 264 XIV
CONTENTS 9 SOLUTIONS OF THE EXERCISES 267 9.1 CHAPTER 1 267 9.2 CHAPTER
2 270 9.3 CHAPTER 3 276 9.4 CHAPTER 4 280 9.5 CHAPTER 5 285 9.6 CHAPTER
6 289 9.7 CHAPTER 7 293 9.8 CHAPTER 8 301 REFERENCES 307 INDEX 311
|
| adam_txt |
ALFIO QUARTERONI FAUSTO SALERI SCIENTIFIC COMPUTING WITH MATLAB AND
OCTAVE SECOND EDITION WITH 108 FIGURES AND 12 TABLES SPRINGER CONTENTS 1
WHAT CAN'T BE IGNORED 1 1.1 REAL NUMBERS 2 1.1.1 HOW WE REPRESENT THEM 2
1.1.2 HOW WE OPERATE WITH FLOATING-POINT NUMBERS 4 1.2 COMPLEX NUMBERS 6
1.3 MATRICES 8 1.3.1 VECTORS 14 1.4 REAL FUNCTIONS 15 1.4.1 THE ZEROS 16
1.4.2 POLYNOMIALS 18 1.4.3 INTEGRATION AND DIFFERENTIATION 21 1.5 TO ERR
IS NOT ONLY HUMAN 23 1.5.1 TALKING ABOUT COSTS 26 1.6 THE MATLAB AND
OCTAVE ENVIRONMENTS 28 1.7 THE MATLAB LANGUAGE 29 1.7.1 MATLAB
STATEMENTS 31 1.7.2 PROGRAMMING IN MATLAB 32 1.7.3 EXAMPLES OF
DIFFERENCES BETWEEN MATLAB AND OCTAVE LANGUAGES 36 1.8 WHAT WE HAVEN'T
TOLD YOU 37 1.9 EXERCISES 37 2 NONLINEAR EQUATIONS 39 2.1 THE BISECTION
METHOD 41 2.2 THE NEWTON METHOD 45 2.2.1 HOW TO TERMINATE NEWTON'S
ITERATIONS 47 2.2.2 THE NEWTON METHOD FOR SYSTEMS OF NONLINEAR EQUATIONS
49 2.3 FIXED POINT ITERATIONS 51 2.3.1 HOW TO TERMINATE FIXED POINT
ITERATIONS 55 XII CONTENTS 2.4 ACCELERATION USING AITKEN METHOD 56 2.5
ALGEBRAIC POLYNOMIALS 60 2.5.1 HOERNER'S ALGORITHM 61 2.5.2 THE
NEWTON-HOERNER METHOD 63 2.6 WHAT WE HAVEN'T TOLD YOU 65 2.7 EXERCISES 67
3 APPROXIMATION OF FUNCTIONS AND DATA 71 3.1 INTERPOLATION 74 3.1.1
LAGRANGIAN POLYNOMIAL INTERPOLATION 75 3.1.2 CHEBYSHEV INTERPOLATION 80
3.1.3 TRIGONOMETRIE INTERPOLATION AND FFT 81 3.2 PIECEWISE LINEAR
INTERPOLATION 86 3.3 APPROXIMATION BY SPLINE FUNCTIONS 88 3.4 THE
LEAST-SQUARES METHOD 92 3.5 WHAT WE HAVEN'T TOLD YOU 97 3.6 EXERCISES 98
4 NUMERICAL DIFFERENTIATION AND INTEGRATION 101 4.1 APPROXIMATION OF
FUNETION DERIVATIVES 103 4.2 NUMERICAL INTEGRATION 105 4.2.1 MIDPOINT
FORMULA 106 4.2.2 TRAPEZOIDAL FORMULA 108 4.2.3 SIMPSON FORMULA 109 4.3
INTERPOLATORY QUADRATURES 111 4.4 SIMPSON ADAPTIVE FORMULA 115 4.5 WHAT
WE HAVEN'T TOLD YOU 119 4.6 EXERCISES 120 5 LINEAR SYSTEMS 123 5.1 THE
LU FACTORIZATION METHOD 126 5.2 THE PIVOTING TECHNIQUE 134 5.3 HOW
AECURATE IS THE LU FACTORIZATION? 136 5.4 HOW TO SOLVE A TRIDIAGONAL
SYSTEM 140 5.5 OVERDETERMINED SYSTEMS 141 5.6 WHAT IS HIDDEN BEHIND THE
COMMAND \ 143 5.7 ITERATIVE METHODS 144 5.7.1 HOW TO CONSTRUET AN
ITERATIVE METHOD 146 5.8 RICHARDSON AND GRADIENT METHODS 150 5.9 THE
CONJUGATE GRADIENT METHOD 153 5.10 WHEN SHOULD AN ITERATIVE METHOD BE
STOPPED? 156 5.11 TO WRAP-UP: DIRECT OR ITERATIVE? 159 5.12 WHAT WE
HAVEN'T TOLD YOU 164 5.13 EXERCISES 164 CONTENTS XIII EIGENVALUES AND
EIGENVECTORS 167 6.1 THE POWER METHOD 170 6.1.1 CONVERGENCE ANALYSIS 173
6.2 GENERALIZATION OF THE POWER METHOD 174 6.3 HOW TO COMPUTE THE SHIFT
176 6.4 COMPUTATION OF ALL THE EIGENVALUES 179 6.5 WHAT WE HAVEN'T TOLD
YOU 183 6.6 EXERCISES 183 ORDINARY DIFFERENTIAL EQUATIONS 187 7.1 THE
CAUCHY PROBLEM 190 7.2 EULER METHODS 191 7.2.1 CONVERGENCE ANALYSIS 194
7.3 THE CRANK-NICOLSON METHOD 197 7.4 ZERO-STABILITY 199 7.5 STABILITY
ON UNBOUNDED INTERVALS 202 7.5.1 THE REGION OF ABSOLUTE STABILITY 204
7.5.2 ABSOLUTE STABILITY CONTROLS PERTURBATIONS 205 7.6 HIGH ORDER
METHODS 212 7.7 THE PREDICTOR-CORRECTOR METHODS 216 7.8 SYSTEMS OF
DIFFERENTIAL EQUATIONS 219 7.9 SOME EXAMPLES 225 7.9.1 THE SPHERICAL
PENDULUM 225 7.9.2 THE THREE-BODY PROBLEM 228 7.9.3 SOME STIFF PROBLEMS
230 7.10 WHAT WE HAVEN'T TOLD YOU 234 7.11 EXERCISES 234 NUMERICAL
METHODS FOR (INITIAL-)BOUNDARY-VALUE PROBLEMS 237 8.1 APPROXIMATION OF
BOUNDARY-VALUE PROBLEMS 240 8.1.1 APPROXIMATION BY FINITE DIFFERENCES
241 8.1.2 APPROXIMATION BY FINITE ELEMENTS 243 8.1.3 APPROXIMATION BY
FINITE DIFFERENCES OF TWO-DIMENSIONAL PROBLEMS 245 8.1.4 CONSISTENCY AND
CONVERGENCE 251 8.2 FINITE DIFFERENCE APPROXIMATION OF THE HEAT EQUATION
. 253 8.3 THE WAVE EQUATION 257 8.3.1 APPROXIMATION BY FINITE
DIFFERENCES 260 8.4 WHAT WE HAVEN'T TOLD YOU 263 8.5 EXERCISES 264 XIV
CONTENTS 9 SOLUTIONS OF THE EXERCISES 267 9.1 CHAPTER 1 267 9.2 CHAPTER
2 270 9.3 CHAPTER 3 276 9.4 CHAPTER 4 280 9.5 CHAPTER 5 285 9.6 CHAPTER
6 289 9.7 CHAPTER 7 293 9.8 CHAPTER 8 301 REFERENCES 307 INDEX 311 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Quarteroni, Alfio 1952- Saleri, Fausto 1965-2007 |
| author_GND | (DE-588)120370158 (DE-588)120434571 |
| author_facet | Quarteroni, Alfio 1952- Saleri, Fausto 1965-2007 |
| author_role | aut aut |
| author_sort | Quarteroni, Alfio 1952- |
| author_variant | a q aq f s fs |
| building | Verbundindex |
| bvnumber | BV021822699 |
| classification_rvk | SK 900 ST 601 |
| classification_tum | DAT 306f MAT 650f |
| ctrlnum | (OCoLC)180902325 (DE-599)BVBBV021822699 |
| dewey-full | 518.1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518.1 |
| dewey-search | 518.1 |
| dewey-sort | 3518.1 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| discipline_str_mv | Informatik Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV021822699 |
| illustrated | Illustrated |
| index_date | 2024-07-02T15:54:44Z |
| indexdate | 2024-07-09T20:45:26Z |
| institution | BVB |
| isbn | 9783540326120 354032612X |
| language | English Italian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015034822 |
| oclc_num | 180902325 |
| open_access_boolean | |
| owner | DE-92 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-83 DE-Aug4 DE-11 |
| owner_facet | DE-92 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-83 DE-Aug4 DE-11 |
| physical | XVI, 318 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| 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 Introduzione al calcolo scientifico Scientific computing with MATLAB and Octave with 12 tables Alfio Quarteroni ; Fausto Saleri 2. ed. Berlin [u.a.] Springer 2006 XVI, 318 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in computational science and engineering 2 Literaturverz. S. 307 - 310 MATLAB Datenverarbeitung Naturwissenschaft Science Data processing Wissenschaftliches Rechnen (DE-588)4338507-2 gnd rswk-swf MATLAB (DE-588)4329066-8 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 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 Texts in computational science and engineering 2 (DE-604)BV016971315 2 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015034822&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 Scientific computing with MATLAB and Octave with 12 tables Texts in computational science and engineering MATLAB Datenverarbeitung Naturwissenschaft Science Data processing Wissenschaftliches Rechnen (DE-588)4338507-2 gnd MATLAB (DE-588)4329066-8 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4338507-2 (DE-588)4329066-8 (DE-588)4042805-9 |
| title | Scientific computing with MATLAB and Octave with 12 tables |
| title_alt | Introduzione al calcolo scientifico |
| title_auth | Scientific computing with MATLAB and Octave with 12 tables |
| title_exact_search | Scientific computing with MATLAB and Octave with 12 tables |
| title_exact_search_txtP | Scientific computing with MATLAB and Octave with 12 tables |
| title_full | Scientific computing with MATLAB and Octave with 12 tables Alfio Quarteroni ; Fausto Saleri |
| title_fullStr | Scientific computing with MATLAB and Octave with 12 tables Alfio Quarteroni ; Fausto Saleri |
| title_full_unstemmed | Scientific computing with MATLAB and Octave with 12 tables Alfio Quarteroni ; Fausto Saleri |
| title_short | Scientific computing with MATLAB and Octave |
| title_sort | scientific computing with matlab and octave with 12 tables |
| title_sub | with 12 tables |
| topic | MATLAB Datenverarbeitung Naturwissenschaft Science Data processing Wissenschaftliches Rechnen (DE-588)4338507-2 gnd MATLAB (DE-588)4329066-8 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | MATLAB Datenverarbeitung Naturwissenschaft Science Data processing Wissenschaftliches Rechnen Numerische Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015034822&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV016971315 |
| work_keys_str_mv | AT quarteronialfio introduzionealcalcoloscientifico AT salerifausto introduzionealcalcoloscientifico AT quarteronialfio scientificcomputingwithmatlabandoctavewith12tables AT salerifausto scientificcomputingwithmatlabandoctavewith12tables |