Algorithms: their complexity and efficiency
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester [u.a.]
Wiley
1987
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Wiley series in computing
A Wiley-Interscience publication |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 363 S. graph. Darst. |
| ISBN: | 0471912018 0471997528 |
Internformat
MARC
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| 100 | 1 | |a Kronsjö, Lydia I. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Algorithms |b their complexity and efficiency |c Lydia Kronsjö |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Chichester [u.a.] |b Wiley |c 1987 | |
| 300 | |a XIII, 363 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Wiley series in computing | |
| 490 | 0 | |a A Wiley-Interscience publication | |
| 650 | 4 | |a Algorithmes | |
| 650 | 7 | |a Algorithmes |2 ram | |
| 650 | 4 | |a Analyse numérique - Informatique | |
| 650 | 7 | |a Analyse numérique |2 ram | |
| 650 | 4 | |a Complexité de calcul (Informatique) | |
| 650 | 7 | |a Complexité de calcul (informatique) |2 ram | |
| 650 | 7 | |a FFT |2 inriac | |
| 650 | 7 | |a Ordinateurs - Programmation |2 ram | |
| 650 | 4 | |a Programmation (Informatique) | |
| 650 | 7 | |a algorithme efficace |2 inriac | |
| 650 | 7 | |a algorithme recherche |2 inriac | |
| 650 | 7 | |a algorithme tri |2 inriac | |
| 650 | 7 | |a complexité algorithme |2 inriac | |
| 650 | 7 | |a multiplication |2 inriac | |
| 650 | 7 | |a processus itératif |2 inriac | |
| 650 | 7 | |a évaluation polynome |2 inriac | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Computational complexity | |
| 650 | 4 | |a Computer algorithms | |
| 650 | 4 | |a Computer programming | |
| 650 | 4 | |a Numerical analysis |x Data processing | |
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Datensatz im Suchindex
| _version_ | 1804116655632023552 |
|---|---|
| adam_text | Contents
1 Introduction 1
1.1 Definition 1
1.2 Measures of Efficiency 2
1.3 Complexity of Algorithms 3
1.4 Computational Complexity of Numerical Algorithms 5
1.5 Numerical Accuracy 6
1.6 Analysis of Algorithms 6
1.7 Bounds of Complexity 8
1.8 Models of Computations 9
2 Evaluation of Polynomials 10
2.1 Polynomial Evaluation Algorithms 10
2.2 Preprocessing the Coefficients 15
2.3 Optimality of the Evaluation Algorithms 17
2.4 Belaga Theorems 20
2.5 Numerical Solution and Conditioning of the Problem 26
2.6 Error Analysis of Evaluation Algorithms 30
2.7 Evaluation of the Derivatives of a Polynomial 35
2.8 Evaluation of a Polynomial with a Complex Argument 38
2.9 Comments 40
Exercises 42
3 Iterative Processes 44
3.1 An Iterative Process 44
3.2 The Newton-Raphson Method: Convergence 47
3.3 Formulation of the Optimality Problem 53
3.4 Iterative Methods with Guaranteed Convergence 55
3.5 Complexity Parameters and Measures of Efficiency 61
3.6 One-point Iterative Methods 64
3.7 Multipoint Iterative Methods 74
3.8 Conditioning of the Root Finding Problem 81
xi
xii
3.9 Iterative Methods for Solving Systems of Non-linear
Equations 82
3.10 Numerical Stability of Iterative Algorithms 85
Exercises 86
4 Direct Methods for Solving Sets of Linear Equations 88
4.1 Gaussian Elimination 89
4.2 Error Analysis 100
4.3 Iterative Refinement of the Solution 108
4.4 Cholesky Decomposition of Symmetric Matrices 110
4.5 The Orthogonal Reduction Methods 114
4.6 How to Speed up Matrix Methods 126
4.7 The Winograd Method 127
4.8 The Strassen Method 136
4.9 Lower Bounds on Matrix Multiplication 143
Exercises 145
5 The Fast Fourier Transform 149
5.1 Introduction 149
5.2 The Continuous Fourier Transform 150
5.3 The Discrete Fourier Transform 152
5.4 The Fast Fourier Transform 157
5.5 The FFT Algorithm for a Non-Uniform Factorization 160
5.6 Optimal Factorization for the FFT 165
5.7 The FFT of Radix 2 167
5.8 DFT for Different Types of Data 175
5.9 Round-off Errors in the FFT 179
5.10 Conclusions 187
Exercises 187
6 Fast Multiplication of Numbers 190
6.1 On the Minimum Computation Time of Functions 190
6.2 The Schonhage-Strassen Algorithm for Multiplying Two
Integers 193
6.3 Multiplication of Two Integers Using Modular Arithmetic 199
6.4 Computing the Reduced Product Coefficients Exactly 201
6.5 Estimation of the Work Involved 207
Exercises 209
7 Internal Sorting 210
7.1 Comparison Sorts 211
7.2 Simple Selection Sort 212
7.3 Heapsort—A Comparison Sort of Complexity n log n 214
7.4 Sorting by Exchange: Bubble Sort 219
xiii
7.5 Quicksort—A Comparison Sort of a Complexity n log n, on
Average 223
7.6 Insertion Sorts 229
7.7 Optimum Comparison Sorting 232
7.8 Lower Bound on the Average Number of Comparisons 237
7.9 Selection of the Ath Largest of n 238
Exercises 243
8 External Sorting 247
8.1 The Two-way Merge 248
8.2 Merge Sorting 252
8.3 The Use of Merge in External Sorting 254
8.4 Polyphase Merge 262
8.5 Cascade Merge 270
8.6 Oscillating Sort 273
8.7 Replacement Selection 274
8.8 Merge Trees and Optimum Merge Sorting 276
8.9 Comments 279
Exercises 280
9 Searching 282
9.1 Introduction 282
9.2 Search Algorithms 283
9.3 Ordered Tables 285
9.4 Search Trees 289
9.5 Search Methods for Unequal Distribution Tables 293
9.6 A Tree Search Followed by Insertion or Deletion of the Key 302
9.7 Balanced Search Trees 305
9.8 Hashing 311
9.9 Collision Resolution by Open Addressing 318
9.10 Performance of the Open Addressing Algorithms 324
9.11 Virtual Hashing 332
Exercises 337
Appendix A 340
Appendix B 347
Bibliography and References 351
Index 359
|
| any_adam_object | 1 |
| author | Kronsjö, Lydia I. |
| author_facet | Kronsjö, Lydia I. |
| author_role | aut |
| author_sort | Kronsjö, Lydia I. |
| author_variant | l i k li lik |
| building | Verbundindex |
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| callnumber-first | Q - Science |
| callnumber-label | QA76 |
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| callnumber-sort | QA 276.6 |
| callnumber-subject | QA - Mathematics |
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| dewey-full | 511 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511 |
| dewey-search | 511 |
| dewey-sort | 3511 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV002200287 |
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| indexdate | 2024-07-09T15:41:58Z |
| institution | BVB |
| isbn | 0471912018 0471997528 |
| language | English |
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| spelling | Kronsjö, Lydia I. Verfasser aut Algorithms their complexity and efficiency Lydia Kronsjö 2. ed. Chichester [u.a.] Wiley 1987 XIII, 363 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in computing A Wiley-Interscience publication Algorithmes Algorithmes ram Analyse numérique - Informatique Analyse numérique ram Complexité de calcul (Informatique) Complexité de calcul (informatique) ram FFT inriac Ordinateurs - Programmation ram Programmation (Informatique) algorithme efficace inriac algorithme recherche inriac algorithme tri inriac complexité algorithme inriac multiplication inriac processus itératif inriac évaluation polynome inriac Datenverarbeitung Computational complexity Computer algorithms Computer programming Numerical analysis Data processing Algorithmus (DE-588)4001183-5 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Datenverarbeitung (DE-588)4011152-0 gnd rswk-swf Algorithmus (DE-588)4001183-5 s Datenverarbeitung (DE-588)4011152-0 s DE-604 Numerische Mathematik (DE-588)4042805-9 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001445341&sequence=000002&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 | Kronsjö, Lydia I. Algorithms their complexity and efficiency Algorithmes Algorithmes ram Analyse numérique - Informatique Analyse numérique ram Complexité de calcul (Informatique) Complexité de calcul (informatique) ram FFT inriac Ordinateurs - Programmation ram Programmation (Informatique) algorithme efficace inriac algorithme recherche inriac algorithme tri inriac complexité algorithme inriac multiplication inriac processus itératif inriac évaluation polynome inriac Datenverarbeitung Computational complexity Computer algorithms Computer programming Numerical analysis Data processing Algorithmus (DE-588)4001183-5 gnd Numerische Mathematik (DE-588)4042805-9 gnd Datenverarbeitung (DE-588)4011152-0 gnd |
| subject_GND | (DE-588)4001183-5 (DE-588)4042805-9 (DE-588)4011152-0 |
| title | Algorithms their complexity and efficiency |
| title_auth | Algorithms their complexity and efficiency |
| title_exact_search | Algorithms their complexity and efficiency |
| title_full | Algorithms their complexity and efficiency Lydia Kronsjö |
| title_fullStr | Algorithms their complexity and efficiency Lydia Kronsjö |
| title_full_unstemmed | Algorithms their complexity and efficiency Lydia Kronsjö |
| title_short | Algorithms |
| title_sort | algorithms their complexity and efficiency |
| title_sub | their complexity and efficiency |
| topic | Algorithmes Algorithmes ram Analyse numérique - Informatique Analyse numérique ram Complexité de calcul (Informatique) Complexité de calcul (informatique) ram FFT inriac Ordinateurs - Programmation ram Programmation (Informatique) algorithme efficace inriac algorithme recherche inriac algorithme tri inriac complexité algorithme inriac multiplication inriac processus itératif inriac évaluation polynome inriac Datenverarbeitung Computational complexity Computer algorithms Computer programming Numerical analysis Data processing Algorithmus (DE-588)4001183-5 gnd Numerische Mathematik (DE-588)4042805-9 gnd Datenverarbeitung (DE-588)4011152-0 gnd |
| topic_facet | Algorithmes Analyse numérique - Informatique Analyse numérique Complexité de calcul (Informatique) Complexité de calcul (informatique) FFT Ordinateurs - Programmation Programmation (Informatique) algorithme efficace algorithme recherche algorithme tri complexité algorithme multiplication processus itératif évaluation polynome Datenverarbeitung Computational complexity Computer algorithms Computer programming Numerical analysis Data processing Algorithmus Numerische Mathematik |
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