Holdings: Scientific computing with MATLAB and Octave

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), Gervasio, Paola (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2010
Edition:	3. ed.
Series:	Texts in computational science and engineering 2
Subjects:	MATLAB Wissenschaftliches Rechnen Numerische Mathematik
Online Access:	Inhaltsverzeichnis
Physical Description:	XVI, 360 S. graph. Darst.
ISBN:	9783642124297

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Record in the Search Index

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adam_text	CONTENTS 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 18 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 . . . . . . . . . . . . . . . . . . . . . . . . . .. 29 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 . . . . . . . . . . . . . . . . . . . . . . . .. 37 1.8 WHAT WE HAVEN T TOLD YOU . . . . . . . . . . . . . . . . . . . . . . . . . .. 38 1.9 EXERCISES.......................................... 38 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 . . . . . . . . . .. 49 2.3.2 THE NEWTON METHOD FOR SYSTEMS OF NONLINEAR EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . .. 51 2.4 FIXED POINT ITERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 54 2.4.1 HOW TO TERMINATE FIXED POINT ITERATIONS 60 XII CONTENTS 2.5 AECELERATION USING AITKEN S METHOD . . . . . . . . . . . .. . . . . .. 60 2.6 ALGEBRAIC POLYNOMIALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 65 2.6.1 HOERNER S ALGORITHM 66 2.6.2 THE NEWTON-HOERNER METHOD . . . . . . . . . . . . . . . . . .. 68 2.7 WHAT WE HAVERI T TOLD YOU , . . . . . . . . . . . . . . .. 70 2.8 EXERCISES.......................................... 72 3 APPROXIMATION OF FUNCTIONS AND DATA . . . . . . . . . . . . . .. .. 75 3.1 SOME REPRESENTATIVE PROBLEMS. . . . . . . . . . . . . . . . . . . . . . .. 75 3.2 APPROXIMATION BY TAYLOR S POLYNOMIALS ..... . . . . . . . . .. 77 3.3 INTERPOLATION....................................... 78 3.3.1 LAGRANGIAN POLYNOMIAL INTERPOLATION. . . . . . . . . . .. 79 3.3.2 STABILITY OF POLYNOMIAL INTERPOLATION. . .. . . . . . . .. 84 3.3.3 INTERPOLATION AT CHEBYSHEV NODES ,.... 86 3.3.4 TRIGONOMETRIE INTERPOLATION AND FFT . . . . . . . . . .. 88 3.4 PIECEWISE LINEAR INTERPOLATION . . . . . . . . . . . . . . . . . . . . . . .. 93 3.5 APPROXIMATION BY SPLINE FUNCTIONS , . . .. 94 3.6 THE LEAST-SQUARES METHOD. . .. . . . . . . . . . . . . . . . . . . . . . . .. 99 3.7 WHAT WE HAVEN T TOLD YOU 103 3.8 EXERCISES 105 4 N UMERICAL DIFFERENTIATION AND INTEGRATION . . . . . .. . . . . . . 107 4.1 SOME REPRESENTATIVE PROBLEMS 107 4.2 APPROXIMATION OF FUNCTION DERIVATIVES 109 4.3 NUMERICAL INTEGRATION 111 4.3.1 MIDPOINT FORMULA 112 4.3.2 TRAPEZOIDAI FORRNULA 114 4.3.3 SIMPSON FORRNULA 115 4.4 INTERPOLATORY QUADRATURES 117 4.5 SIMPSON ADAPTIVE FORMULA . . . . . . . . . . . . . . . . . . . . . . . . . .. 121 4.6 WHAT WE HAVERI T TOLD YOU , 125 4.7 EXERCISES 126 5 LINEAR SYSTEMS , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 5.1 SOME REPRESENTATIVE PROBLEMS 129 5.2 LINEAR SYSTEM AND COMPLEXITY 134 5.3 THE LU FACTORIZATION METHOD 135 5.4 THE PIVOTING TECHNIQUE 144 5.5 HOW ACCURATE IS THE SOLUTION OF A LINEAR SYSTEM? 147 5.6 HOW TO SOLVE A TRIDIAGONAL SYSTEM 150 5.7 OVERDETERMINED SYSTEMS , 152 5.8 WHAT IS HIDDEN BEHIND THE LVIATLAB COMMAND 154 5.9 ITERATIVE METHODS 157 5.9.1 HOW TO CONSTRUCT AN ITERATIVE METHOD 158 CONTENTS XIII 5.10 RICHARDSON AND GRADIENT METHOCLS 162 5.11 THE CONJUGATE GRADIENT METHAD 166 5.12 WHEN SHAULD AN ITERATIVE METHAD BE STAPPED? 169 5.13 TA WRAP-UP: DIRECT OR ITERATIVE? , 171 5.14 WHAT WE HAVENT TOLD YOU , 177 5.15 EXERCISES 1.77 6 EIGENVALUES AND EIGENVEETORS 181 6.1 SOME REPRESENTATIVE PROBLEMS 182 6.2 THE POWER METHOD , 184 6.2.1 CONVERGENCE ANALYSIS , 187 6.3 GENERALIZATION OF THE POWER METHOD 188 6.4 HOW TO COMPUTE THE SHIFT , 190 6.5 COMPUTATION OF ALL THE EIGENVALUES 193 6.6 WHAT WE HAVEN T TOLD YOU 197 6.7 EXERCISES , , , 197 7 ORDINARY DIFFERENTIAL EQUATIONS 201 7.1 SOME REPRESENTATIVE PROBLEMS , 201 7.2 THE CAUCHY PROBLERN , , , 204 7.3 EULER METHODS , . . . . . . . . . . . 205 7.3.1 CONVERGENCE ANALYSIS 208 7.4 THE CRANK-NICOLSON METHOD 212 7.5 ZERO-STABILITY., 214 7.6 STABILITY ON UNBOUNDED INTERVALS 216 7.6.1 THE REGION OF ABSOLUTE STABILITY 219 7.6.2 ABSOLUTE STABILITY CONTROLS PERTURBATIONS 220 7.7 HIGH ORDER METHODS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 7.8 THE PREDICTOR-CORRECTOR METHODS 234 7.9 SYSTEMS OF DIFFERENTIAL EQUATIONS 236 7.10 SOME EXAMPLES 242 7.10.1 THE SPHERICAL PENDULUM 242 7.10.2 THE THREE-BODY PROBLEM 246 7.10.3 SOME STIFF PROBLEMS 248 7.11 WHAT WE HAVEN T TOLD YOU .. , 252 7.12 EXERCISES , 252 8 NUMERICAL APPROXIMATION OF BOUNDARY-VALUE PROBLEMS 255 8.1 SOME REPRESENTATIVE PROBLEMS 256 8.2 APPROXIMATION OF BOUNDARY-VALUE PROBLEMS 258 8.2.1 FINITE DIFFERENCE APPROXIMATION OF THE ONE-DIMENSIONAL POISSON PROBLEM 259 8.2.2 FINITE DIFFERENCE APPROXIMATION OF A CONVECTION-DOMINATED PROBLEM 262 XIV CONTENTS 8.2.3 FINITE ELEMENT APPROXIMATION OF THE ONE-DIMENSIONAL POISSON PROBLEM 263 8.2.4 FINITE DIFFERENCE APPROXIMATION OF THE TWO-DIMENSIONAL POISSON PROBLEM 267 8.2.5 CONSISTENCY AND CONVERGENCE OF FINITE DIFFERENCE DISCRETIZATION OF THE POISSON PROBLEM 272 8.2.6 FINITE DIFFERENCE APPROXIMATION OF THE ONE-DIMENSIONAL HEAT EQUATION .. . . . . . . . . . . . . . .. 274 8.2.7 FINITE ELEMENT APPROXIMATION OF THE ONE-DIMENSIONAL HEAT EQUATION .. . . . . . . . . . . . . . . . 278 8.3 HYPERBOLIC EQUATIONS: A SCALAR PURE ADVECTION PROBLEM .. 281 8.3.1 FINITE DIFFERENCE DISCRETIZATION OF THE SCALAR TRANSPORT EQUATION. . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 8.3.2 FINITE DIFFERENCE ANALYSIS FOR THE SCALAR TRANSPORT EQUATION 285 8.3.3 FINITE ELEMENT SPACE DISCRETIZATION OF THE SCALAR ADVECTION EQUATION 292 8.4 THE WAVE EQUATION 293 8.4.1 FINITE DIFFERENCE APPROXIMATION OF THE WAVE EQUATION 295 8.5 WHAT WE HAVEN T TOLD YOU 299 8.6 EXERCISES 300 9 SOLUTIONS OF THE EXERCISES 303 9.1 CHAPTER 1 303 9.2 CHAPTER 2 - - 306 9.3 CHAPTER 3 312 9.4 CHAPTER 4 315 9.5 CHAPTER 5 320 9.6 CHAPTER 6 327 9.7 CHAPTER 7 - - 330 9.8 CHAPTER 8 - 339 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 347 INDEX 353
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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 ; Paola Gervasio 3. ed. Berlin [u.a.] Springer 2010 XVI, 360 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in computational science and engineering 2 MATLAB (DE-588)4329066-8 gnd rswk-swf Wissenschaftliches Rechnen (DE-588)4338507-2 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-101 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 978-3-642-12430-3 Texts in computational science and engineering 2 (DE-604)BV016971315 2 OEBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020485028&sequence=000003&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 with 12 tables Texts in computational science and engineering MATLAB (DE-588)4329066-8 gnd Wissenschaftliches Rechnen (DE-588)4338507-2 gnd Numerische Mathematik (DE-588)4042805-9 gnd
subject_GND	(DE-588)4329066-8 (DE-588)4338507-2 (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 ; Paola Gervasio
title_fullStr	Scientific computing with MATLAB and Octave with 12 tables Alfio Quarteroni ; Fausto Saleri ; Paola Gervasio
title_full_unstemmed	Scientific computing with MATLAB and Octave with 12 tables Alfio Quarteroni ; Fausto Saleri ; Paola Gervasio
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 (DE-588)4329066-8 gnd Wissenschaftliches Rechnen (DE-588)4338507-2 gnd Numerische Mathematik (DE-588)4042805-9 gnd
topic_facet	MATLAB Wissenschaftliches Rechnen Numerische Mathematik
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020485028&sequence=000003&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 gervasiopaola introduzionealcalcoloscientifico AT quarteronialfio scientificcomputingwithmatlabandoctavewith12tables AT salerifausto scientificcomputingwithmatlabandoctavewith12tables AT gervasiopaola scientificcomputingwithmatlabandoctavewith12tables

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MARC

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