Introduction to numerical analysis:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | German English |
| Veröffentlicht: |
New York [u.a.]
Springer
1996
|
| Ausgabe: | 2. ed., corr. 3. print. |
| Schriftenreihe: | Texts in applied mathematics
12 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XIII, 660 S. graph. Darst. |
| ISBN: | 354097878X 038797878X |
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| 240 | 1 | 0 | |a Einführung in die numerische Mathematik |
| 245 | 1 | 0 | |a Introduction to numerical analysis |c J. Stoer ; R. Bulirsch. Transl. by R. Bartels ... |
| 250 | |a 2. ed., corr. 3. print. | ||
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Datensatz im Suchindex
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| adam_text | J. STOER R. BULIRSCH INTRODUCTION TO NUMERICAL ANALYSIS SECOND EDITION
TRANSLATED BY R. BARTELS, W. GAUTSCHI, AND C. WITZGALL WITH 35
ILLUSTRATIONS SPRINGER CONTENTS PREFACE TO THE SECOND EDITION V PREFACE
TO THE FIRST EDITION VII 1 ERROR ANALYSIS 1 1.1 REPRESENTATION OF
NUMBERS 2 1.2 ROUNDOFF ERRORS AND FLOATING-POINT ARITHMETIC 5 1.3 ERROR
PROPAGATION 9 1.4 EXAMPLES 20 1.5 INTERVAL ARITHMETIC; STATISTICAL
ROUNDOFF ESTIMATION 27 EXERCISES FOR CHAPTER 1 33 REFERENCES FOR CHAPTER
1 36 2 INTERPOLATION 37 2.1 INTERPOLATION BY POLYNOMIALS 38 2.1.1
THEORETICAL FOUNDATION: THE INTERPOLATION FORMULA OF LAGRANGE 38 2.1.2
NEVILLE S ALGORITHM 40 2.1.3 NEWTON S INTERPOLATION FORMULA: DIVIDED
DIFFERENCES 43 2.1.4 THE ERROR IN POLYNOMIAL INTERPOLATION 49 2.1.5
HERMITE INTERPOLATION 52 2.2 INTERPOLATION BY RATIONAL FUNCTIONS 58
2.2.1 GENERAL PROPERTIES OF RATIONAL INTERPOLATION 58 2.2.2 INVERSE AND
RECIPROCAL DIFFERENCES. THIELE S CONTINUED FRACTION 63 2.2.3 ALGORITHMS
OF THE NEVILLE TYPE 67 2.2.4 COMPARING RATIONAL AND POLYNOMIAL
INTERPOLATIONS 71 2.3 TRIGONOMETRIC INTERPOLATION 72 IX 2.3.1 BASIC
FACTS 72 2.3.2 FAST FOURIER TRANSFORMS 78 2.3.3 THE ALGORITHMS OF
GOERTZEL AND REINSCH 84 2.3.4 THE CALCULATION OF FOURIER COEFFICIENTS.
ATTENUATION FACTORS 88 2.4 INTERPOLATION BY SPLINE FUNCTIONS 93 2.4.1
THEORETICAL FOUNDATIONS 93 2.4.2 DETERMINING INTERPOLATING CUBIC SPLINE
FUNCTIONS 97 2.4.3 CONVERGENCE PROPERTIES OF CUBIC SPLINE FUNCTIONS 102
2.4.4 B-SPLINES 107 2.4.5 THE COMPUTATION OF B-SPLINES 110 EXERCISES FOR
CHAPTER 2 114 REFERENCES FOR CHAPTER 2 123 3 TOPICS IN INTEGRATION 3.1
THE INTEGRATION FORMULAS OF NEWTON AND COTES 126 3.2 PEANO S ERROR
REPRESENTATION 131 3.3 THE EULER-MACLAURIN SUMMATION FORMULA 135 3.4
INTEGRATING BY EXTRAPOLATION 139 3.5 ABOUT EXTRAPOLATION METHODS 144 3.6
GAUSSIAN INTEGRATION METHODS 150 3.7 INTEGRALS WITH SINGULARITIES 160
EXERCISES FOR CHAPTER 3 162 REFERENCES FOR CHAPTER 3 166 4 SYSTEMS OF
LINEAR EQUATIONS 4.1 GAUSSIAN ELIMINATION. THE TRIANGULAR DECOMPOSITION
OF A MATRIX 4.2 THE GAUSS-JORDAN ALGORITHM 177 4.3 THE CHOLESKY
DECOMPOSITION 180 4.4 ERROR BOUNDS 183 4.5 ROUNDOFF-ERROR ANALYSIS FOR
GAUSSIAN ELIMINATION 191 4.6 ROUNDOFF ERRORS IN SOLVING TRIANGULAR
SYSTEMS 196 4.7 ORTHOGONALIZATION TECHNIQUES OF HOUSEHOLDER AND
GRAM-SCHMIDT 4.8 DATA FITTING 205 4.8.1 LINEAR LEAST SQUARES. THE NORMAL
EQUATIONS 207 4.8.2 THE USE OF ORTHOGONALIZATION IN SOLVING LINEAR
LEAST-SQUARES PROBLEMS 209 4.8.3 THE CONDITION OF THE LINEAR
LEAST-SQUARES PROBLEM 210 4.8.4 NONLINEAR LEAST-SQUARES PROBLEMS 217
4.8.5 THE PSEUDOINVERSE OF A MATRIX 218 4.9 MODIFICATION TECHNIQUES FOR
MATRIX DECOMPOSITIONS 221 4.10 THE SIMPLEX METHOD 230 4.11 PHASE ONE OF
THE SIMPLEX METHOD 241 APPENDIX TO CHAPTER 4 245 4.A ELIMINATION METHODS
FOR SPARSE MATRICES 245 EXERCISES FOR CHAPTER 4 253 REFERENCES FOR
CHAPTER 4 258 CONTENTS XI 5 FINDING ZEROS AND MINIMUM POINTS BY
ITERATIVE METHODS 260 5.1 THE DEVELOPMENT OF ITERATIVE METHODS 261 5.2
GENERAL CONVERGENCE THEOREMS 264 5.3 THE CONVERGENCE OF NEWTON S METHOD
IN SEVERAL VARIABLES 269 5.4 A MODIFIED NEWTON METHOD 272 5.4.1 ON THE
CONVERGENCE OF MINIMIZATION METHODS 273 5.4.2 APPLICATION OF THE
CONVERGENCE CRITERIA TO THE MODIFIED NEWTON METHOD 278 5.4.3 SUGGESTIONS
FOR A PRACTICAL IMPLEMENTATION OF THE MODIFIED NEWTON METHOD. A RANK-ONE
METHOD DUE TO BROYDEN 282 5.5 ROOTS OF POLYNOMIALS. APPLICATION OF
NEWTON S METHOD 286 5.6 STURM SEQUENCES AND BISECTION METHODS 297 5.7
BAIRSTOW S METHOD 301 5.8 THE SENSITIVITY OF POLYNOMIAL ROOTS 303 5.9
INTERPOLATION METHODS FOR DETERMINING ROOTS 306 5.10 THEA 2
-METHODOFAITKEN 312 5.11 MINIMIZATION PROBLEMS WITHOUT CONSTRAINTS 316
EXERCISES FOR CHAPTER 5 325 REFERENCES FOR CHAPTER 5 328 6 EIGENVALUE
PROBLEMS 330 6.0 INTRODUCTION 330 6.1 BASIC FACTS ON EIGENVALUES 332 6.2
THE JORDAN NORMAL FORM OF A MATRIX 335 6.3 THE FROBENIUS NORMAL FORM OF
A MATRIX 340 6.4 THE SCHUR NORMAL FORM OF A MATRIX; HERMITIAN AND NORMAL
MATRICES; SINGULAR VALUES OF MATRICES 345 6.5 REDUCTION OF MATRICES TO
SIMPLER FORM 351 6.5.1 REDUCTION OF A HERMITIAN MATRIX TO TRIDIAGONAL
FORM: THE METHOD OF HOUSEHOLDER 353 6.5.2 REDUCTION OF A HERMITIAN
MATRIX TO TRIDIAGONAL OR DIAGONAL FORM: THE METHODS OF GIVENS AND JACOBI
358 6.5.3 REDUCTION OF A HERMITIAN MATRIX TO TRIDIAGONAL FORM: THE
METHOD OF LANCZOS 362 . 6.5.4 REDUCTION TO HESSENBERG FORM 366 6.6
METHODS FOR DETERMINING THE EIGENVALUES AND EIGENVECTORS 370 6.6.1
COMPUTATION OF THE EIGENVALUES OF A HERMITIAN TRIDIAGONAL MATRIX 370
6.6.2 COMPUTATION OF THE EIGENVALUES OF A HESSENBERG MATRIX. THE METHOD
OF HYMAN 372 6.6.3 SIMPLE VECTOR ITERATION AND INVERSE ITERATION OF
WIELANDT 373 6.6.4 THE LR AND QR METHODS 380 6.6.5 THE PRACTICAL
IMPLEMENTATION OFTHESSAE METHOD 389 6.7 COMPUTATION OF THE SINGULAR VALUES
OF A MATRIX 400 6.8 GENERALIZED EIGENVALUE PROBLEMS 405 6.9 ESTIMATION
OF EIGENVALUES 406 EXERCISES FOR CHAPTER 6 419 REFERENCES FOR CHAPTER 6
425 7 ORDINARY DIFFERENTIAL EQUATIONS 428 7.0 INTRODUCTION 428 7.1 SOME
THEOREMS FROM THE THEORY OF ORDINARY DIFFERENTIAL EQUATIONS 430 7.2
INITIAL-VALUE PROBLEMS 434 7.2.1 ONE-STEP METHODS: BASIC CONCEPTS 434
7.2.2 CONVERGENCE OF ONE-STEP METHODS 439 7.2.3 ASYMPTOTIC EXPANSIONS
FOR THE GLOBAL DISCRETIZATION ERROR OF ONE-STEP METHODS 443 7.2.4 THE
INFLUENCE OF ROUNDING ERRORS IN ONE-STEP METHODS 445 7.2.5 PRACTICAL
IMPLEMENTATION OF ONE-STEP METHODS 448 7.2.6 MULTISTEP METHODS: EXAMPLES
455 7.2.7 GENERAL MULTISTEP METHODS 458 7.2.8 AN EXAMPLE OF DIVERGENCE
461 7.2.9 LINEAR DIFFERENCE EQUATIONS 464 7.2.10 CONVERGENCE OF
MULTISTEP METHODS 467 7.2.11 LINEAR MULTISTEP METHODS 471 7.2.12
ASYMPTOTIC EXPANSIONS OF THE GLOBAL DISCRETIZATION ERROR FOR LINEAR
MULTISTEP METHODS 476 7.2.13 PRACTICAL IMPLEMENTATION OF MULTISTEP
METHODS 481 7.2.14 EXTRAPOLATION METHODS FOR THE SOLUTION OF THE
INITIAL-VALUE PROBLEM 484 7.2.15 COMPARISON OF METHODS FOR SOLVING
INITIAL-VALUE PROBLEMS 487 7.2.16 STIFF DIFFERENTIAL EQUATIONS 488
7.2.17 IMPLICIT DIFFERENTIAL EQUATIONS. DIFFERENTIAL-ALGEBRAIC EQUATIONS
494 7.3 BOUNDARY-VALUE PROBLEMS 499 7.3.0 INTRODUCTION 499 7.3.1 THE
SIMPLE SHOOTING METHOD 502 7.3.2 THE SIMPLE SHOOTING METHOD FOR LINEAR
BOUNDARY-VALUE PROBLEMS 507 7.3.3 AN EXISTENCE AND UNIQUENESS THEOREM
FOR THE SOLUTION OF BOUNDARY-VALUE PROBLEMS 509 7.3.4 DIFFICULTIES IN
THE EXECUTION OF THE SIMPLE SHOOTING METHOD 511 7.3.5 THE MULTIPLE
SHOOTING METHOD 516 7.3.6 HINTS FOR THE PRACTICAL IMPLEMENTATION OF THE
MULTIPLE SHOOTING METHOD 520 7.3.7 AN EXAMPLE: OPTIMAL CONTROL PROGRAM
FOR A LIFTING REENTRY SPACE VEHICLE 524 7.3.8 THE LIMITING CASE M -* OO
OF THE MULTIPLE SHOOTING METHOD (GENERAL NEWTON S METHOD,
QUASILINEARIZATION) 531 7.4 DIFFERENCE METHODS 535 7.5 VARIATIONAL
METHODS 540 7.6 COMPARISON OF THE METHODS FOR SOLVING BOUNDARY-VALUE
PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS 549 7.7 VARIATIONAL METHODS
FOR PARTIAL DIFFERENTIAL EQUATIONS. THE FINITE-ELEMENT METHOD 553
EXERCISES FOR CHAPTER 7 560 REFERENCES FOR CHAPTER 7 566 CONTENTS ** 8
ITERATIVE METHODS FOR THE SOLUTION OF LARGE SYSTEMS OF LINEAR EQUATIONS.
SOME FURTHER METHODS 570 8.0 INTRODUCTION 570 8.1 GENERAL PROCEDURES FOR
THE CONSTRUCTION OF ITERATIVE METHODS 571 8.2 CONVERGENCE THEOREMS 574
8.3 RELAXATION METHODS 579 8.4 APPLICATIONS TO DIFFERENCE METHODS*AN
EXAMPLE 588 8.5 BLOCK ITERATIVE METHODS 594 8.6 THE ADI-METHOD OF
PEACEMAN AND RACHFORD 597 8.7 THE CONJUGATE-GRADIENT METHOD OF HESTENES
AND STIEFEL 606 8.8 THE ALGORITHM OF BUNEMAN FOR THE SOLUTION OF THE
DISCRETIZED POISSON EQUATION 614 8.9 MULTIGRID METHODS 622 8.10
COMPARISON OF ITERATIVE METHODS 632 EXERCISES FOR CHAPTER 8 636
REFERENCES FOR CHAPTER 8 643 GENERAL LITERATURE ON NUMERICAL METHODS 646
INDEX 648
|
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| author | Stoer, Josef 1934- Bulirsch, Roland |
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| author_facet | Stoer, Josef 1934- Bulirsch, Roland |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 900 |
| ctrlnum | (OCoLC)35121949 (DE-599)BVBBV011146998 |
| dewey-full | 519.420 519.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-search | 519.4 20 519.4 |
| dewey-sort | 3519.4 220 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed., corr. 3. print. |
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| isbn | 354097878X 038797878X |
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| physical | XIII, 660 S. graph. Darst. |
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| spelling | Stoer, Josef 1934- Verfasser (DE-588)105888052 aut Einführung in die numerische Mathematik Introduction to numerical analysis J. Stoer ; R. Bulirsch. Transl. by R. Bartels ... 2. ed., corr. 3. print. New York [u.a.] Springer 1996 XIII, 660 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in applied mathematics 12 Literaturangaben Analise numerica larpcal Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Numerische Mathematik (DE-588)4042805-9 s DE-604 Bulirsch, Roland Verfasser aut Texts in applied mathematics 12 (DE-604)BV002476038 12 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007471631&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stoer, Josef 1934- Bulirsch, Roland Introduction to numerical analysis Texts in applied mathematics Analise numerica larpcal Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4123623-3 |
| title | Introduction to numerical analysis |
| title_alt | Einführung in die numerische Mathematik |
| title_auth | Introduction to numerical analysis |
| title_exact_search | Introduction to numerical analysis |
| title_full | Introduction to numerical analysis J. Stoer ; R. Bulirsch. Transl. by R. Bartels ... |
| title_fullStr | Introduction to numerical analysis J. Stoer ; R. Bulirsch. Transl. by R. Bartels ... |
| title_full_unstemmed | Introduction to numerical analysis J. Stoer ; R. Bulirsch. Transl. by R. Bartels ... |
| title_short | Introduction to numerical analysis |
| title_sort | introduction to numerical analysis |
| topic | Analise numerica larpcal Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Analise numerica Numerical analysis Numerische Mathematik Lehrbuch |
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