Handbook of numerical analysis: 3 Techniques of scientific computing (part 1). Numerical methods for solids (part 1). Solution of equations in Rn (part 2)
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| Format: | Book |
| Language: | English |
| Published: |
Amsterdam
North-Holland
1994
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| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 778 S. graph. Darst. |
| ISBN: | 0444899286 |
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MARC
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| 245 | 1 | 0 | |a Handbook of numerical analysis |n 3 |p Techniques of scientific computing (part 1). Numerical methods for solids (part 1). Solution of equations in Rn (part 2) |c general editor: P. G. Ciarlet (Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie), J. L. Lions |
| 264 | 1 | |a Amsterdam |b North-Holland |c 1994 | |
| 300 | |a X, 778 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 700 | 1 | |a Ciarlet, Philippe G. |d 1938- |e Sonstige |0 (DE-588)143368362 |4 oth | |
| 700 | 1 | |a Lions, Jacques-Louis |d 1928-2001 |e Sonstige |0 (DE-588)124055397 |4 oth | |
| 700 | 1 | |a Du, Qiang |d 1964- |0 (DE-588)1188249320 |4 edt | |
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Record in the Search Index
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| adam_text | Contents
Chaptf.r I. Interpolation 7
1. Polynomial interpolation 7
2. Pade approximation 9
3. Rational interpolation 11
4. Spline interpolation 12
5. Multivariate interpolation 14
6. The general interpolation problem 15
Chapter II. Approximation 17
7. Linear approximation 18
8. Nonlinear approximation 21
9. Multivariate approximation 23
Chapter III. Numerical Quadrature 25
10. Newton Cotes formulae 26
11. Gaussian quadratures 29
12. Cubatures 32
References 33
Subject Index 45
Contents
Preface 51
Chapter I. Algebraic Theory 53
1. Introduction 53
2. Definitions 55
3. Algebraic properties 61
4. Formal orthogonal polynomials 64
5. Adjacent families of orthogonal polynomials 68
6. Recursive computation of Pade approximants 71
7. The ^ algorithm 74
8. Continued fractions 75
9. Error estimation 77
10. Duality 85
11. The method of moments 88
Chapter II. Convergence 93
12. Introduction to the convergence problem 93
13. Meromorphic functions 99
14. Functions with smooth Taylor series coefficients. Entire functions 106
15. Stieltjes series 110
16. Polya frequency series 120
17. Convergence in capacity 121
18. Inverse problem 126
Chapter III. Generalizations 131
19. Pade type approximants 131
20. Partial Pade approximants 140
21. Multipoint Pade approximants 151
22. Cauchy type approximants 157
23. Series of functions 161
24. Pade Hermite approximants 167
25. Vector Pade approximants 169
26. The noncommutative case 176
27. Multivariate approximants 180
Chapter IV. Applications 193
28. The exponential function 193
29. ,4 acceptable approximations to the exponential function 195
30. Borel transform 198
31. z transform 200
32. Laplace transform inversion 203
49
50 C. Brezinski and J. Van Iseghem
References 213
Subject Index 221
Contents
Preface 227
Chapter I. Interpolation 229
1. Interpolation of functions 229
2. Lagrange s interpolation polynomial 232
3. Divided differences and Newton interpolation polynomial 234
4. Aitken s scheme 238
5. Finite differences 239
6. Interpolation polynomials with finite differences 241
7. Frazer s diagram (Lozenge diagram) 245
8. Utilization of the interpolation formulas 246
9. Inverse interpolation 247
10. The Hermite Birkhoff interpolation problem (H B problem) 248
11. The Abel Gontcharov interpolation problem (A G problem) 252
12. The Hermite interpolation problem (H problem) 254
13. The divided differences with repeating knots and Hermite interpolation 257
14. Interpolation by means of trigonometric polynomials 262
15. Interpolation of complex functions 266
16. Chakalov s approach for divided differences 270
17. Interpolation of functions of several variables 274
18. Multivariate Hermite interpolation 281
19. Convergence of the interpolation processes 284
20. The Lagrange interpolation process 284
21. Discrete Fourier transforms 289
22. Fast Fourier transforms (FFTs) 290
23. Applications of FFTs 295
Chapter II. Uniform Approximation 301
24. Uniform distance and best approximation 301
25. Characterization of the element of the best approximation 304
26. Uniqueness of the polynomial of the best uniform approximation 309
27. The uniform rational approximation
28. The Vallee Poussin and Chebyshev theorems for rational functions 313
29. The possibility for approximation of continuous functions 316
30. Moduli of functions 317
30.1. Moduli of smoothness 318
30.2. Integral moduli 319
30.3. Averaged moduli 320
31. Approximation of functions by means of linear operators 323
32. Whitney s theorem 325
33. On the order of the uniform approximation by polynomials 333
34. Newman s results and approximation by means of rational functions 339
225
226 Bl. Sendov and A. Andreev
35. Chebyshev polynomials 342
36. Approximation of functions on a discrete point set 347
37. The discrete Remez algorithm 354
38. The second Remez algorithm 357
39. Remez algorithm—Multidimensional case 360
40. A second Remez algorithm for rational functions 365
41. The differential correction algorithm 367
42. Algorithms for rational approximation 372
43. Stability of numerical methods 374
Chapter III. Numerical Integration 381
44. Quadrature formulas 381
45. Optimal knots 386
46. An estimate of the error of quadrature formulas 392
47. Estimates for classical quadrature formulas 395
48. Quadrature formulas with restrictions 397
49. The Runge principle. Romberg s quadrature formulas 399
50. Integration of periodic functions 401
51. Obreshkov Chakalov quadrature formulas 403
52. A concept for the best quadrature formulas 404
53. Monte Carlo methods 406
53.1. Convergence and error of the MC method 407
54. Ordinary and geometric MC methods for integrals 408
54.1. Ordinary MC method 408
54.2. Geometric MC method 409
55. Effective MC methods 410
55.1. Separation of the principal part 411
55.2. Symmetrization of the integrand 411
55.3. Important sampling method 412
56. MC methods with increased rate of convergence 412
57. Random interpolation quadrature formulas 414
58. Quasi MC methods 416
59. MC methods for continual integrals, weight functions, splitting method 418
59.1. Continual integrals 418
59.2. Weight functions 420
59.3. Splitting method 421
Chapter IV. Hausdorff Approximation 423
60. Segment functions and Hausdorff distance 423
61. The metric space Fu and H distance in Au 425
62. Relationships between the uniform distance and the Hausdorff distance 427
63. Convergence of sequences of positive operators 429
64. Approximation of periodic functions by positive integral operators 431
65. Approximation by partial sums of Fourier series 434
66. The best Hausdorff approximation 438
67. Universal estimates 442
68. Numerical methods for calculating the polynomial of best Hausdorff approximation 443
69. Multidimensional Hausdorff approximation 447
References 451
Subject Index 461
Contents
Preface 469
Chapter I. Mechanical Models 471
1. Kinematics 471
2. Deformation invariants and special cases 473
3. The equations of equilibrium 474
4. Constitutive laws 476
4.1. Hyperelastic compressible materials 477
4.2. Hyperelastic incompressible materials 481
4.3. Nearly incompressible materials 483
Chapter II. Mathematical Analysis 485
5. Definition of the boundary value problem 487
6. Examples of solutions 488
7. Weak formulations of equilibrium problems 490
7.1. The compressible case 490
7.2. The incompressible case 491
8. The minimization approach 493
9. Existence results by minimization arguments 498
10. Existence results by differential calculus 501
Chapter III. Approximation Theory 507
11. Approximation of compressible problems 508
12. Approximation of incompressible problems 511
13. Approximation of nearly incompressible problems 513
14. Linearization and compatibility condition 515
15. Existence and convergence results IV
16. Convergence in the compressible case 526
17. Additional remarks on the convergence theorems 527
Chapter IV. Numerical Solution Techniques 529
18. The system to solve 530
19. The basic Newton s method 533
20. Newton s method with incremental loading 535
21. Arc length continuation 539
21.1. General presentation 539
21.2. Arclength continuation: Detailed algorithm 541
21.3. Extended Newton s algorithm 543
22. On the solution of the linear system (S) _ 544
23. On the choice of the stored energy function W 545
24. Conclusion 546
467
468 P Le Tallec
Chapter V. Augmented Lagrangian Methods 549
25. Introduction of a new discrete formulation 549
26. Basic iterative method 553
27. The problems in displacements 554
28. The local problems in deformation gradients 556
28.1. Formulation and preliminary lemma 556
28.2. Solution procedure 557
29. Numerical results 560
29.1. Stretching of a cracked rectangular bar 561
29.2. Postbuckling solution of a three dimensional beam 561
Chapter VI. Equilibrium Problems with Frictionless Contact 565
30. Formulation of a contact problem 566
31. Existence results 570
32. Finite element discretization 572
33. A first numerical algorithm 573
34. The nonlinear programming approach 575
35. Extensions to self contact 577
Chapter VII. Extension to Viscoelasticity 579
36. The rheological model 580
37. Thermodynamical model 581
38. Mathematical formulation 584
38.1. The complete nonlinear model 584
38.2. Choosing the free energy potential 585
38.3. Linearization 586
39. Approximation in space 588
39.1. Galerkin approximation 588
39.2. Linearized problems 589
39.3. Transformation of the linearized problems 590
39.4. Main result 591
39.5. Technical theorems 593
39.6. Proof of the main result 598
40. Discretization in time 601
40.1. Approximation in time 601
40.2. Convergence theory 601
41. Numerical solution 603
41.1. Basic algorithm .603
41.2. Numerical implementation 605
41.3. Numerical tests 606
42. Conclusion 607
Rl FKRl NCKS 611
List of Symbols 617
Subject Index 621
Contents
Preface 629
Chapter I. Properties of Algebraic Equations 631
1. Existence of the roots 631
2. Newton s formula and symmetric functions 635
3. Resolvent and discriminant of polynomials 637
4. Algebraic equations from first till fourth degree 639
5. Number of roots in an interval 640
6. Number of roots in a domain 645
7. Algebraic equations with a negative real part of the roots 648
8. Number of roots in a disc 650
9. The Gauss Lucas theorem and Sendov s conjecture 651
10. Distribution of the roots on the plane 654
Chapter II. Localization Bounds 657
11. Elementary bounds 657
12. Estimations of the unique positive root 673
13. Sendov s method for localization of all positive roots 683
Chapter III. Local and Global Methods 687
14. Bernoulli s iteration 687
15. Graeffe s method 689
16. The method of Laguerre 693
17. The Lehmer Schur method 697
Chapter IV. Iterative Methods for Computation of All Roots 699
18. Iterative methods without derivatives 699
19. Iterative methods with derivatives 710
20. Simultaneous approximation of multiple roots 724
21. Multi point methods for simultaneous approximation 733
22. Factorization of a polynomial 735
23. Interval methods for polynomial root determining 739
Chapter V. Computational Complexity (Renegar and Neff Approach) 747
24. Definitions and notation 747
25. The lower bound (Renegar approach) 748
26. Algorithm for the upper bound (Neff approach) 752
27. Approximate factorization
627
628 Bl. Sendov, A. Andreev and N. Kjurkchiev
28. q Splittings of the complex plane 756
29. Approximating the factors by contour integration 759
30. Finding a balanced splitting point 762
References 767
Subject Index 777
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| institution | BVB |
| isbn | 0444899286 |
| language | English |
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| spelling | Handbook of numerical analysis 3 Techniques of scientific computing (part 1). Numerical methods for solids (part 1). Solution of equations in Rn (part 2) general editor: P. G. Ciarlet (Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie), J. L. Lions Amsterdam North-Holland 1994 X, 778 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Ciarlet, Philippe G. 1938- Sonstige (DE-588)143368362 oth Lions, Jacques-Louis 1928-2001 Sonstige (DE-588)124055397 oth Du, Qiang 1964- (DE-588)1188249320 edt (DE-604)BV002745459 3 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006506402&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Handbook of numerical analysis |
| title | Handbook of numerical analysis |
| title_auth | Handbook of numerical analysis |
| title_exact_search | Handbook of numerical analysis |
| title_full | Handbook of numerical analysis 3 Techniques of scientific computing (part 1). Numerical methods for solids (part 1). Solution of equations in Rn (part 2) general editor: P. G. Ciarlet (Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie), J. L. Lions |
| title_fullStr | Handbook of numerical analysis 3 Techniques of scientific computing (part 1). Numerical methods for solids (part 1). Solution of equations in Rn (part 2) general editor: P. G. Ciarlet (Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie), J. L. Lions |
| title_full_unstemmed | Handbook of numerical analysis 3 Techniques of scientific computing (part 1). Numerical methods for solids (part 1). Solution of equations in Rn (part 2) general editor: P. G. Ciarlet (Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie), J. L. Lions |
| title_short | Handbook of numerical analysis |
| title_sort | handbook of numerical analysis techniques of scientific computing part 1 numerical methods for solids part 1 solution of equations in rn part 2 |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006506402&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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