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Scientific computing with MATLAB and Octave: with 12 tables

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Bibliographic Details
Main Authors:	Quarteroni, Alfio 1952- (Author), Saleri, Fausto 1965-2007 (Author)
Format:	Book
Language:	English Italian
Published:	Berlin [u.a.] Springer 2006
Edition:	2. ed.
Series:	Texts in computational science and engineering 2
Subjects:	MATLAB Datenverarbeitung Naturwissenschaft Science > Data processing Wissenschaftliches Rechnen Numerische Mathematik
Links:	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
Item Description:	Literaturverz. S. 307 - 310
Physical Description:	XVI, 318 S. graph. Darst.
ISBN:	9783540326120 354032612X

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Record in the Search Index

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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
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author	Quarteroni, Alfio 1952- Saleri, Fausto 1965-2007
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isbn	9783540326120 354032612X
language	English Italian
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series	Texts in computational science and engineering
series2	Texts in computational science and engineering
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_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

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