Applied numerical methods using MATLAB:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Hoboken, NJ
Wiley-Interscience
2005
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 509 S. graph. Darst. |
| ISBN: | 0471698334 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804133258252779520 |
|---|---|
| adam_text | APPLIED NUMERICAL METHODS USING MATLAB WON YOUNG YANG CHUNG-ANG
UNIVERSITY, KOREA WENWU CAO PENNSYLVANIA STATE UNIVERSITY TAE-SANG CHUNG
CHUNG-ANG UNIVERSITY, KOREA JOHN MORRIS THE UNIVERSITY OF AUCKLAND, NEW
ZEALAND WILEY- INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION
CONTENTS PREFACE XIII 1 MATLAB USAGE AND COMPUTATIONAL ERRORS 1 1.1
BASIC OPERATIONS OF MATLAB / 1 1.1.1 INPUT/OUTPUT OF DATA FROM MATLAB
COMMAND WINDOW / 2 1.1.2 INPUT/OUTPUT OF DATA THROUGH FILES / 2 1.1.3
INPUT/OUTPUT OF DATA USING KEYBOARD / 4 1.1.4 2-D GRAPHIC INPUT/OUTPUT /
5 1.1.5 3-D GRAPHIC OUTPUT / 10 1.1.6 MATHEMATICAL FUNCTIONS / 10 1.1.7
OPERATIONS ON VECTORS AND MATRICES / 15 1.1.8 RANDOM NUMBER GENERATORS /
22 1.1.9 FLOW CONTROL / 24 1.2 COMPUTER ERRORS VERSUS HUMAN MISTAKES /
27 1.2.1 IEEE 64-BIT FLOATING-POINT NUMBER REPRESENTATION / 28 1.2.2
VARIOUS KINDS OF COMPUTING ERRORS / 31 1.2.3 ABSOLUTE/RELATIVE COMPUTING
ERRORS / 33 1.2.4 ERROR PROPAGATION / 33 1.2.5 TIPS FOR AVOIDING LARGE
ERRORS / 34 1.3 TOWARD GOOD PROGRAM / 37 1.3.1 NESTED COMPUTING FOR
COMPUTATIONAL EFNCIENCY / 37 1.3.2 VECTOR OPERATION VERSUS LOOP
ITERATION / 39 1.3.3 ITERATIVE ROUTINE VERSUS NESTED ROUTINE / 40 1.3.4
TO AVOID RUNTIME ERROR / 40 1.3.5 PARAMETER SHARING VIA GLOBAL VARIABLES
/ 44 1.3.6 PARAMETER PASSING THROUGH VARARGIN / 45 1.3.7 ADAPTIVE INPUT
ARGUMENT LIST / 46 PROBLEMS / 46 VII VUEI CONTENTS 2 SYSTEM OF LINEAR
EQUATIONS 2.1 SOLUTION FOR A SYSTEM OF LINEAR EQUATIONS / 72 2.1.1 THE
NONSINGULAR CASE (M = N) I 72 2.1.2 THE UNDERDETERMINED CASE (M N):
MINIMUM-NORM SOLUTION / 72 2.1.3 THE OVERDETERMINED CASE (M N):
LEAST-SQUARES ERROR SOLUTION / 75 2.1.4 RLSE (RECURSIVE LEAST-SQUARES
ESTIMATION) / 76 2.2 SOLVING A SYSTEM OF LINEAR EQUATIONS / 79 2.2.1
GAUSS ELIMINATION / 79 2.2.2 PARTIAL PIVOTING / 81 2.2.3 GAUSS-JORDAN
ELIMINATION / 89 2.3 INVERSE MATRIX / 92 2.4 DECOMPOSITION
(FACTORIZATION) / 92 2.4.1 LU DECOMPOSITION (FACTORIZATION):
TRIANGULARIZATION / 92 2.4.2 OTHER DECOMPOSITION (FACTORIZATION):
CHOLESKY, QR, AND SVD / 97 2.5 ITERATIVE METHODS TO SOLVE EQUATIONS / 98
2.5.1 JACOBI ITERATION / 98 2.5.2 GAUSS-SEIDEL ITERATION / 100 2.5.3 THE
CONVERGENCE OF JACOBI AND GAUSS-SEIDEL ITERATIONS / 103 PROBLEMS / 104 3
INTERPOLATION AND CURVE FITTING 3.1 INTERPOLATION BY LAGRANGE POLYNOMIAL
/ 117 3.2 INTERPOLATION BY NEWTON POLYNOMIAL / 119 3.3 APPROXIMATION BY
CHEBYSHEV POLYNOMIAL / 124 3.4 PADE APPROXIMATION BY RATIONAL FUNCTION /
129 3.5 INTERPOLATION BY CUBIC SPLINE / 133 3.6 HERMITE INTERPOLATING
POLYNOMIAL / 139 3.7 TWO-DIMENSIONAL INTERPOLATION / 141 3.8 CURVE
FITTING / 143 3.8.1 STRAIGHT LINE FIT: A POLYNOMIAL FUNCTION OF FIRST
DEGREE / 144 3.8.2 POLYNOMIAL CURVE FIT: A POLYNOMIAL FUNCTION OF HIGHER
DEGREE / 145 3.8.3 EXPONENTIAL CURVE FIT AND OTHER FUNCTIONS / 149 3.9
FOURIER TRANSFORM / 150 3.9.1 FFT VERSUS DFT / 151 3.9.2 PHYSICAL
MEANING OF DFT / 152 3.9.3 INTERPOLATION BY USING DFS / 155 PROBLEMS /
157 CONTENTS IX 4 NONLINEAR EQUATIONS 179 4.1 ITERATIVE METHOD TOWARD
FIXED POINT / 179 4.2 BISECTION METHOD / 183 4.3 FALSE POSITION OR
REGULA FALSI METHOD / 185 4.4 NEWTON(-RAPHSON) METHOD / 186 4.5 SECANT
METHOD / 189 4.6 NEWTON METHOD FOR A SYSTEM OF NONLINEAR EQUATIONS / 191
4.7 SYMBOLIC SOLUTION FOR EQUATIONS / 193 4.8 A REAL-WORLD PROBLEM / 194
PROBLEMS / 197 5 NUMERICAL DIFFERENTIATION/INTEGRATION 209 5.1
DIFFERENCE APPROXIMATION FOR FIRST DERIVATIVE / 209 5.2 APPROXIMATION
ERROR OF FIRST DERIVATIVE / 211 5.3 DIFFERENCE APPROXIMATION FOR SECOND
AND HIGHER DERIVATIVE / 216 5.4 INTERPOLATING POLYNOMIAL AND NUMERICAL
DIFFERENTIAL / 220 5.5 NUMERICAL INTEGRATION AND QUADRATURE / 222 5.6
TRAPEZOIDAL METHOD AND SIMPSON METHOD / 226 5.7 RECURSIVE RULE AND
ROMBERG INTEGRATION / 228 5.8 ADAPTIVE QUADRATURE / 231 5.9 GAUSS
QUADRATURE / 234 5.9.1 GAUSS-LEGENDRE INTEGRATION / 235 5.9.2
GAUSS-HERMITE INTEGRATION / 238 5.9.3 GAUSS-LAGUERRE INTEGRATION / 239
5.9.4 GAUSS-CHEBYSHEV INTEGRATION / 240 5.10 DOUBLE INTEGRAL / 241
PROBLEMS / 244 6 ORDINARY DIFFERENTIAL EQUATIONS 263 6.1 EULER S METHOD
/ 263 6.2 HEUN S METHOD: TRAPEZOIDAL METHOD / 266 6.3 RUNGE-KUTTA METHOD
/ 267 6.4 PREDICTOR-CORRECTOR METHOD / 269 6.4.1 ADAMS-BASHFORTH-MOULTON
METHOD / 269 6.4.2 HAMMING METHOD / 273 6.4.3 COMPARISON OF METHODS /
274 6.5 VECTOR DIFFERENTIAL EQUATIONS / 277 6.5.1 STATE EQUATION / 277
6.5.2 DISCRETIZATION OF LTI STATE EQUATION / 281 6.5.3 HIGH-ORDER
DIFFERENTIAL EQUATION TO STATE EQUATION / 283 6.5.4 STIFF EQUATION / 284
X CONTENTS 6.6 BOUNDARY VALUE PROBLEM (BVP) / 287 6.6.1 SHOOTING METHOD
/ 287 6.6.2 FINITE DIFFERENCE METHOD / 290 PROBLEMS / 293 7 OPTIMIZATION
321 7.1 UNCONSTRAINED OPTIMIZATION [L-2, CHAPTER 7] / 321 7.1.1 GOLDEN
SEARCH METHOD / 321 7.1.2 QUADRATIC APPROXIMATION METHOD / 323 7.1.3
NELDER-MEAD METHOD [W-8] / 325 7.1.4 STEEPEST DESCENT METHOD / 328 7.1.5
NEWTON METHOD / 330 7.1.6 CONJUGATE GRADIENT METHOD / 332 7.1.7
SIMULATED ANNEALING METHOD [W-7] / 334 7.1.8 GENETIC ALGORITHM [W-7] /
338 7.2 CONSTRAINED OPTIMIZATION [L-2, CHAPTER 10] / 343 7.2.1 LAGRANGE
MULTIPLIER METHOD / 343 7.2.2 PENALTY FUNCTION METHOD / 346 7.3 MATLAB
BUILT-IN ROUTINES FOR OPTIMIZATION / 350 7.3.1 UNCONSTRAINED
OPTIMIZATION / 350 7.3.2 CONSTRAINED OPTIMIZATION / 352 7.3.3 LINEAR
PROGRAMMING (LP) / 355 PROBLEMS / 357 8 MATRICES AND EIGENVALUES 371 8.1
EIGENVALUES AND EIGENVECTORS / 371 8.2 SIMILARITY TRANSFORMATION AND
DIAGONALIZATION / 373 8.3 POWER METHOD / 378 8.3.1 SCALED POWER METHOD /
378 8.3.2 INVERSE POWER METHOD / 380 8.3.3 SHIFTED INVERSE POWER METHOD
/ 380 8.4 JACOBI METHOD / 381 8.5 PHYSICAL MEANING OF
EIGENVALUES/EIGENVECTORS / 385 8.6 EIGENVALUE EQUATIONS / 389 PROBLEMS /
390 9 PARTIAL DIFFERENTIAL EQUATIONS 401 9.1 ELLIPTIC PDE / 402 9.2
PARABOLIC PDE / 406 9.2.1 THE EXPLICIT FORWARD EULER METHOD / 406 9.2.2
THE IMPLICIT BACKWARD EULER METHOD / 407 CONTENTS XI 9.2.3 THE
CRANK-NICHOLSON METHOD / 409 9.2.4 TWO-DIMENSIONAL PARABOLIC PDE / 412
9.3 HYPERBOLIC PDE / 414 9.3.1 THE EXPLICIT CENTRAL DIFFERENCE METHOD /
415 9.3.2 TWO-DIMENSIONAL HYPERBOLIC PDE / 417 9.4 FINITE ELEMENT METHOD
(FEM) FOR SOLVING PDE / 420 9.5 GUI OF MATLAB FOR SOLVING PDES: PDETOOL
/ 429 9.5.1 BASIC PDES SOLVABLE BY PDETOOL / 430 9.5.2 THE USAGE OF
PDETOOL / 431 9.5.3 EXAMPLES OF USING PDETOOL TO SOLVE PDES / 435
PROBLEMS / 444 APPENDIX A. MEAN VALUE THEOREM 461 APPENDIX B. MATRIX
OPERATIONS/PROPERTIES 463 APPENDIX C. DIFFERENTIATION WITH RESPECT TO A
VECTOR 471 APPENDIX D. LAPLACE TRANSFORM 473 APPENDIX E. FOURIER
TRANSFORM 475 APPENDIX F. USEFUL FORMULAS 477 APPENDIX G. SYMBOLIC
COMPUTATION 481 APPENDIX H. SPARSE MATRICES 489 APPENDIX I. MATLAB 491
REFERENCES 497 SUBJECT INDEX 499 INDEX FOR MATLAB ROUTINES 503 INDEX FOR
TABLES 509
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| indexdate | 2024-07-09T20:05:51Z |
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| isbn | 0471698334 |
| language | English |
| lccn | 2004013108 |
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| spelling | Applied numerical methods using MATLAB Won Young Yang ... Hoboken, NJ Wiley-Interscience 2005 XIV, 509 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier aMATLAB Analyse numérique - Informatique MATLAB gtt Numerieke wiskunde gtt aNumerical analysis xData processing Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf MATLAB (DE-588)4329066-8 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 s MATLAB (DE-588)4329066-8 s DE-604 Yang, Won-yong Sonstige oth GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013102267&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Applied numerical methods using MATLAB aMATLAB Analyse numérique - Informatique MATLAB gtt Numerieke wiskunde gtt aNumerical analysis xData processing Numerische Mathematik (DE-588)4042805-9 gnd MATLAB (DE-588)4329066-8 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4329066-8 |
| title | Applied numerical methods using MATLAB |
| title_auth | Applied numerical methods using MATLAB |
| title_exact_search | Applied numerical methods using MATLAB |
| title_full | Applied numerical methods using MATLAB Won Young Yang ... |
| title_fullStr | Applied numerical methods using MATLAB Won Young Yang ... |
| title_full_unstemmed | Applied numerical methods using MATLAB Won Young Yang ... |
| title_short | Applied numerical methods using MATLAB |
| title_sort | applied numerical methods using matlab |
| topic | aMATLAB Analyse numérique - Informatique MATLAB gtt Numerieke wiskunde gtt aNumerical analysis xData processing Numerische Mathematik (DE-588)4042805-9 gnd MATLAB (DE-588)4329066-8 gnd |
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