Multiscale, nonlinear and adaptive approximation: dedicated to Wolfgang Dahmen on the occasion of his 60th birthday
Gespeichert in:
| Weitere beteiligte Personen: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2009
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018653977&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XXIII, 659 S. Ill., graph. Darst. 24 cm |
| ISBN: | 9783642034121 |
Internformat
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| 245 | 1 | 0 | |a Multiscale, nonlinear and adaptive approximation |b dedicated to Wolfgang Dahmen on the occasion of his 60th birthday |c Ronald A. DeVore ... ed. |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2009 | |
| 300 | |a XXIII, 659 S. |b Ill., graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
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| 600 | 1 | 7 | |a Dahmen, Wolfgang |d 1949- |0 (DE-588)130554235 |2 gnd |9 rswk-swf |
| 650 | 4 | |a Approximation - Aufsatzsammlung | |
| 650 | 4 | |a Numerische Mathematik - Aufsatzsammlung | |
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| 655 | 7 | |0 (DE-588)4006432-3 |a Bibliografie |2 gnd-content | |
| 655 | 7 | |0 (DE-588)4016928-5 |a Festschrift |2 gnd-content | |
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| 700 | 1 | |a Dahmen, Wolfgang |d 1949- |0 (DE-588)130554235 |4 hnr | |
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Datensatz im Suchindex
| _version_ | 1819345625488031744 |
|---|---|
| adam_text | CONTENTS INTRODUCTION: WOLFGANG DAHMEN S MATHEMATICAL WORK 1 RONALD A.
DEVORE AND ANGELA KUNOTH 1 INTRODUCTION 1 2 THE EARLY YEARS: CLASSICAL
APPROXIMATION THEORY 2 3 BONN, BIELEFELD, BERLIN, AND MULTIVARIATE
SPLINES 2 3.1 COMPUTER AIDED GEOMETRIC DESIGN 3 3.2 SUBDIVISION AND
WAVELETS 4 4 WAVELET AND MULTISCALE METHODS FOR OPERATOR EQUATIONS 5 4.1
MULTILEVEL PRECONDITIONING 5 4.2 COMPRESSION OF OPERATORS 5 5 ADAPTIVE
SOLVERS 6 6 CONSTRUCTION AND IMPLEMENTATION 7 7 HYPERBOLIC PARTIAL
DIFFERENTIAL EQUATIONS AND CONSERVATION LAWS ... 8 8 ENGINEERING
COLLABORATIONS 9 9 THE PRESENT 9 10 FINAL REMARKS 10 PUBLICATIONS BY
WOLFGANG DAHMEN (AS OF SUMMER 2009) 10 THE WAY THINGS WERE IN
MULTIVARIATE SPLINES: A PERSONAL VIEW 19 CARL DE BOOR 1 TENSOR PRODUCT
SPLINE INTERPOLATION 19 2 QUASIINTERPOLATION 20 3 MULTIVARIATE B-SPLINES
21 4 KERGIN INTERPOLATION 23 5 THE RECURRENCE FOR MULTIVARIATE B-SPLINES
25 6 POLYHEDRAL SPLINES 27 7 BOX SPLINES 28 8 SMOOTH MULTIVARIATE
PIECEWISE POLYNOMIALS AND THE B-NET 31 REFERENCES 34 BIBLIOGRAFISCHE
INFORMATIONEN HTTP://D-NB.INFO/996247378 DIGITALISIERT DURCH XII
CONTENTS ON THE EFFICIENT COMPUTATION OF HIGH-DIMENSIONAL INTEGRALS AND
THE APPROXIMATION BY EXPONENTIAL SUMS 39 DIETRICH BRAESS AND WOLFGANG
HACKBUSCH 1 INTRODUCTION 39 2 APPROXIMATION OF COMPLETELY MONOTONE
FUNCTIONS BY EXPONENTIAL SUMS 41 3 RATIONAL APPROXIMATION OF THE SQUARE
ROOT FUNCTION 43 3.1 HERON S ALGORITHM AND GAUSS ARITHMETIC-GEOMETRIC
MEAN 43 3.2 HERON S METHOD AND BEST RATIONAL APPROXIMATION 44 3.3
EXTENSION OF THE ESTIMATE (19) 48 3.4 AN EXPLICIT FORMULA 49 4
APPROXIMATION OF 1 /X A BY EXPONENTIAL SUMS 50 4.1 APPROXIMATION OF 1 /X
ON FINITE INTERVALS 50 4.2 APPROXIMATION OF 1 /X ON [ 1, ») 51 4.3
APPROXIMATION OF 1 /X A , A 0 54 5 APPLICATIONS OF 1/JC APPROXIMATIONS
55 5.1 ABOUT THE EXPONENTIAL SUMS 55 5.2 APPLICATION IN QUANTUM
CHEMISTRY 55 5.3 INVERSE MATRIX 56 6 APPLICATIONS OF /Y/X
APPROXIMATIONS 58 6.1 BASIC FACTS 58 6.2 APPLICATION TO CONVOLUTION 58
6.3 MODIFICATION FOR WAVELET APPLICATIONS 60 6.4 EXPECTATION VALUES OF
THE H-ATOM 60 7 COMPUTATION OF THE BEST APPROXIMATION 62 8 RATIONAL
APPROXIMATION OF SFX CONTENTS XIII 3.4 THE CASE OF SMOOTH FUNCTIONS 95 4
ANISOTROPIE PIECEWISE CONSTANT APPROXIMATION ON RECTANGLES 100 4.1 A
HEURISTIC ESTIMATE 100 4.2 A RIGOUROUS ESTIMATE 103 5 ANISOTROPIE
PIECEWISE POLYNOMIAL APPROXIMATION 108 5.1 THE SHAPE FUNCTION 108 5.2
ALGEBRAIC EXPRESSIONS OF THE SHAPE FUNCTION 109 5.3 ERROR ESTIMATES ILL
5.4 ANISOTROPIE SMOOTHNESS AND CARTOON FUNCTIONS 112 6 ANISOTROPIE
GREEDY REFINEMENT ALGORITHMS 116 6.1 THE REFINEMENT ALGORITHM FOR
PIECEWISE CONSTANTS ON RECTANGLES 119 6.2 CONVERGENCE OF THE ALGORITHM
121 6.3 OPTIMAL CONVERGENCE 124 6.4 REFINEMENT ALGORITHMS FOR PIECEWISE
POLYNOMIALS ON TRIANGLES 128 REFERENCES 134 ANISOTROPIE FUNCTION SPACES
WITH APPLICATIONS 137 SHAI DEKEL AND PENCHO PETRUSHEV 1 INTRODUCTION 137
2 ANISOTROPIE MULTISCALE STRUCTURES ON W 139 2.1 ANISOTROPIE MULTILEVEL
ELLIPSOID COVERS (DILATIONS) OF W .139 2.2 COMPARISON OF ELLIPSOID
COVERS WITH NESTED TRIANGULATIONS IN M 2 142 3 BUILDING BLOCKS 143 3.1
CONSTRUCTION OF A MULTILEVEL SYSTEM OF BASES 143 3.2 COMPACTLY SUPPORTED
DUALS AND LOCAL PROJECTORS 145 3.3 TWO-LEVEL-SPLIT BASES 146 3.4 GLOBAL
DUALS AND POLYNOMIAL REPRODUCING KERNELS 148 3.5 CONSTRUCTION OF
ANISOTROPIC WAVELET FRAMES 151 3. XIV CONTENTS NONLINEAR APPROXIMATION
AND ITS APPLICATIONS 169 RONALD A. DEVORE 1 THE EARLY YEARS 169 2
SMOOTHNESS AND INTERPOLATION SPACES 171 2.1 THE ROLE OF INTERPOLATION
172 3 THE MAIN TYPES OF NONLINEAR APPROXIMATION 174 3.1 N-TERM
APPROXIMATION 174 3.2 ADAPTIVE APPROXIMATION 178 3.3 TREE APPROXIMATION
178 3.4 GREEDY ALGORITHMS 181 4 IMAGE COMPRESSION 185 5 REMARKS ON
NONLINEAR APPROXIMATION IN PDE SOLVERS 187 6 LEARNING THEORY 189 6.1
LEARNING WITH GREEDY ALGORITHMS 193 7 COMPRESSED SENSING 195 8 FINAL
THOUGHTS 199 REFERENCES 199 UNIVARIATE SUBDIVISION AND MULTI-SCALE
TRANSFORMS: THE NONLINEAR CASE .. 203 NIRA DYN AND PETER OSWALD 1
INTRODUCTION 203 2 NONLINEAR MULTI-SCALE TRANSFORMS: FUNCTIONAL SETTING
210 2.1 BASIC NOTATION AND FURTHER EXAMPLES 210 2.2 POLYNOMIAL
REPRODUCTION AND DERIVED SUBDIVISION SCHEMES 215 2.3 CONVERGENCE AND
SMOOTHNESS 217 2.4 STABILITY 223 2.5 APPROXIMATION ORDER AND DECAY OF
DETAILS 227 3 THE GEOMETRIC SETTING: CASE STUDIES 230 3.1 GEOMETRY-BASED
SUBDIVISION SCHEMES 231 3.2 GEOMETRIC MULTI-SCALE TRANSFORMS FOR PLANAR
CURVES 240 REFERENCES 245 RAPID SOLUTION OF BOUNDARY INTEGRAL EQUATIONS
BY WAVELET GALERKIN SCHEMES 249 HELMUT HARBRECHT AND REINHOLD SCHNEIDER
1 INTRODUCTION 249 2 CONTENTS XV 3.5 PATCHWISE SMOOTH WAVELET BASES 266
3.6 GLOBALLY CONTINUOUS WAVELET BASES 267 4 THE WAVELET GALERKIN SCHEME
271 4.1 HISTORICAL NOTES 272 4.2 DISCRETIZATION 273 4.3 A-PRIORI
COMPRESSION 274 4.4 SETTING UP THE COMPRESSION PATTERN 275 4.5
COMPUTATION OF MATRIX COEFFICIENTS 277 4.6 A-POSTERIORI COMPRESSION 279
4.7 WAVELET PRECONDITIONING 279 4.8 NUMERICAL RESULTS 281 4.9 ADAPTIVITY
284 REFERENCES 290 LEARNING OUT OF LEADERS 295 GERARD KERKYACHARIAN,
MATHILDE MOUGEOT, DOMINIQUE PICARD AND KARINE TRIBOULEY 1 INTRODUCTION
295 2 VARIOUS LEARNING ALGORITHMS IN WOLFGANG DAHMEN S WORK 298 2.1
GREEDY LEARNING ALGORITHMS 298 2.2 TREE THRESHOLDING PROCEDURES 299 3
LEARNING OUT LEADERS: LOL 303 3.1 GAUSSIAN REGRESSION MODEL 303 3.2 LOL
PROCEDURE 304 3.3 SPARSITY CONDITIONS ON THE TARGET FUNCTION / 305 3.4
RESULTS 306 3.5 DISCUSSION 307 3.6 RESTRICTED LOL 308 4 PRACTICAL
PERFORMANCES OF THE LOL PROCEDURE 309 4.1 EXPERIMENTAL DESIGN 309 4.2
ALGORITHM 310 4.3 SIMULATION RESULTS 312 4.4 QUALITY RECONSTRUCTION 313
4.5 DISCUSSION 314 5 PROOFS 316 5.1 PRELIMINARIES 316 5.2 CONCENTRATION
LEMMA 5.4 318 5.3 PROOF OF THEOREM 3.2 319 REFERENCES 323 OPTIMIZED
WAVELET PRECONDITIONING 325 ANGEL XVI CONTENTS 2.3 SADDLE POINT PROBLEMS
INVOLVING ESSENTIAL BOUNDARY CONDITIONS 331 2.4 PDE-CONSTRAINED CONTROL
PROBLEMS: DISTRIBUTED CONTROL .. 334 2.5 PDE-CONSTRAINED CONTROL
PROBLEMS: DIRICHLET BOUNDARY CONTROL 336 3 WAVELETS 337 3.1 BASIC
PROPERTIES 337 3.2 NORM EQUIVALENCES AND RIESZ MAPS 340 3.3
REPRESENTATION OF OPERATORS 341 3.4 MULTISCALE DECOMPOSITION OF FUNCTION
SPACES 342 4 PROBLEMS IN WAVELET COORDINATES 356 4.1 ELLIPTIC BOUNDARY
VALUE PROBLEMS 356 4.2 SADDLE POINT PROBLEMS 358 4.3 CONTROL PROBLEMS:
DISTRIBUTED CONTROL 361 4.4 CONTROL PROBLEMS: DIRICHLET BOUNDARY CONTROL
365 5 ITERATIVE SOLUTION 367 5.1 FINITE SYSTEMS ON UNIFORM GRIDS 368 5.2
NUMERICAL EXAMPLES 372 REFERENCES 376 MULTIRESOLUTION SCHEMES FOR
CONSERVATION LAWS 379 SIEGFRIED MUELLER 1 INTRODUCTION 379 2 GOVERNING
EQUATIONS AND FINITE VOLUME SCHEMES 381 3 MULTISCALE ANALYSIS 383 4
MULTISCALE-BASED SPATIAL GRID ADAPTATION 387 5 ADAPTIVE MULTIRESOLUTION
FINITE VOLUME SCHEMES 389 5.1 FROM THE REFERENCE SCHEME TO AN ADAPTIVE
SCHEME 389 5.2 APPROXIMATE FLUX AND SOURCE APPROXIMATION STRATEGIES ..
390 5.3 PREDICTION STRATEGIES 392 5.4 MULTILEVEL TIME STEPPING 393 5.5
ERROR ANALYSIS 397 6 NUMERICAL RESULTS 397 6.1 THE SOLVER QUADFLOW 398
6.2 APPLICATION 398 7 CONCLUSION AND TRENDS 402 REFERENCE CONTENTS 2.3
THE INF-SUP THEORY 419 2.4 TWO SPECIAL PROBLEM CLASSES 423 2.5
APPLICATIONS 427 2.6 PROBLEMS 430 3 THE PETROV-GALERKIN METHOD AND
FINITE ELEMENT BASES 432 3.1 PETROV-GALERKIN SOLUTIONS 433 3.2 FINITE
ELEMENT SPACES 438 3.3 PROBLEMS 445 4 MESH REFINEMENT BY BISECTION 447
4.1 SUBDIVISION OF A SINGLE SIMPLEX 447 4.2 MESH REFINEMENT BY BISECTION
451 4.3 BASIC PROPERTIES OF TRIANGULATIONS 454 4.4 REFINEMENT ALGORITHMS
457 4.5 COMPLEXITY OF REFINEMENT BY BISECTION 462 4.6 PROBLEMS 468 5
PIECEWISE POLYNOMIAL APPROXIMATION 469 5.1 QUASI-INTERPOLATION 469 5.2 A
PRIORI ERROR ANALYSIS 472 5.3 PRINCIPLE OF ERROR EQUIDISTRIBUTION 474
5.4 ADAPTIVE APPROXIMATION 476 5.5 PROBLEMS 479 6 A POSTERIORI ERROR
ANALYSIS 480 6.1 ERROR AND RESIDUAL 481 6.2 GLOBAL UPPER BOUND 482 6.3
LOWER BOUNDS 487 6.4 PROBLEMS 495 7 ADAPTIVITY: CONVERGENCE 497 7.1 THE
ADAPTIVE ALGORITHM 497 7.2 DENSITY AND CONVERGENCE 499 7.3 PROPERTIES OF
THE PROBLEM AND THE MODULES 501 7.4 CONVERGENCE 503 7.5 PROBLEMS 511 8
ADAPTIVITY: CONTRACTION PROPERTY 512 8.1 THE MODULES OF AFEM FOR THE
MODEL PROBLEM 513 8.2 PROPERTIES OF THE MODULES OF AFEM 514 8.3
CONTRACTION PROPERTY OF AFEM 518 8.4 EXAMPLE: DISCONTINUOUS COEFFICIENTS
520 8.5 PROBLEMS 522 9 ADAPTIVITY: CONVERGENCE RATES 524 9. XVIII
CONTENTS ADAPTIVE WAVELET METHODS FOR SOLVING OPERATOR EQUATIONS: AN
OVERVIEW 543 ROB STEVENSON 1 INTRODUCTION 543 1.1 NON-ADAPTIVE METHODS
543 1.2 ADAPTIVE METHODS 545 1.3 BEST AF-TERM APPROXIMATION AND
APPROXIMATION CLASSES .. 546 1.4 STRUCTURE OF THE PAPER 547 1.5 SOME
PROPERTIES OF THE (QUASI-) NORMS || * ||JM 547 2 WELL-POSED LINEAR
OPERATOR EQUATIONS 549 2.1 REFORMULATION AS A BI-INFINITE MATRIX VECTOR
EQUATION .... 549 2.2 SOME MODEL EXAMPLES 550 3 ADAPTIVE WAVELET SCHEMES
I: INEXACT RICHARDSON ITERATION 552 3.1 RICHARDSON ITERATION 552 3.2
PRACTICAL SCHEME 553 3.3 THE ROUTINES COARSE AND APPLY 558 3.4
NON-COERCIVE B 562 3.5 ALTERNATIVES FOR THE RICHARDSON ITERATION 564 4
ADAPTIVE WAVELET SCHEMES II: THE ADAPTIVE WAVELET-GALERKIN METHOD 565
4.1 THE ADAPTIVE WAVELET-GALERKIN METHOD (AWGM) IN A IDEALIZED SETTING
565 4.2 PRACTICAL SCHEME 568 4.3 DISCUSSION 574 5 THE APPROXIMATION OF
OPERATORS IN WAVELET COORDINATES BY COMPUTABLE SPARSE MATRICES 574 5.1
NEAR-SPARSITY OF PARTIAL DIFFERENTIAL OPERATORS IN WAVELET COORDINATES
575 5.2 THE APPROXIMATE COMPUTATION OF THE SIGNIFICANT ENTRIES .. 580
5.3 TREES 583 6 ADAPTIVE FRAME METHODS 585 6.1 INTRODUCTION 585 6.
CONTENTS XIX 7.8 OTHER, NON-ELLIPTIC PROBLEMS 594 REFERENCES 594 OPTIMAL
MULTILEVEL METHODS FOR //(GRAD), //(CURL), AND //(DIV) SYSTEMS ON GRADED
AND UNSTRUCTURED GRIDS 599 JINCHAO XU, LONG CHEN, AND RICARDO H.
NOCHETTO 1 INTRODUCTION 599 2 THE METHOD OF SUBSPACE CORRECTIONS 601 2.1
ITERATIVE METHODS 602 2.2 SPACE DECOMPOSITION AND METHOD OF SUBSPACE
CORRECTION 604 2.3 SHARP CONVERGENCE IDENTITIES 607 3 MULTILEVEL METHODS
ON QUASI-UNIFORM GRIDS 609 3.1 FINITE ELEMENT METHODS 609 3.2 MULTILEVEL
SPACE DECOMPOSITION AND MULTIGRID METHOD... 611 3.3 STABLE DECOMPOSITION
AND OPTIMALITY OF BPX PRECONDITIONER 612 3.4 UNIFORM CONVERGENCE OF
V-CYCLE MULTIGRID 616 3.5 SYSTEMS WITH STRONGLY DISCONTINUOUS
COEFFICIENTS 618 4 MULTILEVEL METHODS ON GRADED GRIDS 621 4.1 BISECTION
METHODS 622 4.2 COMPATIBLE BISECTIONS 624 4.3 DECOMPOSITION OF BISECTION
GRIDS 625 4.4 GENERATION OF COMPATIBLE BISECTIONS 627 4.5 NODE-ORIENTED
COARSENING ALGORITHM 629 4.6 SPACE DECOMPOSITION ON BISECTION GRIDS 630
4.7 STRENGTHENED CAUCHY-SCHWARZ INEQUALITY 634 4.8 BPX PRECONDITIONER
AND MULTIGRID ON GRADED BISECTION GRIDS 636 5 MULTILEVEL METHODS FOR
H(CURL) AND H(DIV) SYSTEMS 636 5.1 PRELIMINARIES 638 5.2 SPACE
DECOMPOSITION AND MULTIGRID METHODS 646 5.3 STABLE DECOMPOSITION 648 6
THE AUXILIARY SPACE METHOD AND HX PRECONDITIONER FOR UNSTRUCTURE
|
| any_adam_object | 1 |
| author2 | DeVore, Ronald A. 1941- |
| author2_role | edt |
| author2_variant | r a d ra rad |
| author_GND | (DE-588)108077969 (DE-588)130554235 |
| author_facet | DeVore, Ronald A. 1941- |
| building | Verbundindex |
| bvnumber | BV035794722 |
| classification_rvk | SK 540 |
| ctrlnum | (OCoLC)444898495 (DE-599)DNB996247378 |
| discipline | Mathematik |
| format | Book |
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| genre | (DE-588)4143413-4 Aufsatzsammlung gnd-content (DE-588)4006432-3 Bibliografie gnd-content (DE-588)4016928-5 Festschrift gnd-content |
| genre_facet | Aufsatzsammlung Bibliografie Festschrift |
| id | DE-604.BV035794722 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T14:00:21Z |
| institution | BVB |
| isbn | 9783642034121 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018653977 |
| oclc_num | 444898495 |
| open_access_boolean | |
| owner | DE-824 |
| owner_facet | DE-824 |
| physical | XXIII, 659 S. Ill., graph. Darst. 24 cm |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| spellingShingle | Multiscale, nonlinear and adaptive approximation dedicated to Wolfgang Dahmen on the occasion of his 60th birthday Dahmen, Wolfgang 1949- (DE-588)130554235 gnd Approximation - Aufsatzsammlung Numerische Mathematik - Aufsatzsammlung Numerische Mathematik (DE-588)4042805-9 gnd Approximation (DE-588)4002498-2 gnd |
| subject_GND | (DE-588)130554235 (DE-588)4042805-9 (DE-588)4002498-2 (DE-588)4143413-4 (DE-588)4006432-3 (DE-588)4016928-5 |
| title | Multiscale, nonlinear and adaptive approximation dedicated to Wolfgang Dahmen on the occasion of his 60th birthday |
| title_auth | Multiscale, nonlinear and adaptive approximation dedicated to Wolfgang Dahmen on the occasion of his 60th birthday |
| title_exact_search | Multiscale, nonlinear and adaptive approximation dedicated to Wolfgang Dahmen on the occasion of his 60th birthday |
| title_full | Multiscale, nonlinear and adaptive approximation dedicated to Wolfgang Dahmen on the occasion of his 60th birthday Ronald A. DeVore ... ed. |
| title_fullStr | Multiscale, nonlinear and adaptive approximation dedicated to Wolfgang Dahmen on the occasion of his 60th birthday Ronald A. DeVore ... ed. |
| title_full_unstemmed | Multiscale, nonlinear and adaptive approximation dedicated to Wolfgang Dahmen on the occasion of his 60th birthday Ronald A. DeVore ... ed. |
| title_short | Multiscale, nonlinear and adaptive approximation |
| title_sort | multiscale nonlinear and adaptive approximation dedicated to wolfgang dahmen on the occasion of his 60th birthday |
| title_sub | dedicated to Wolfgang Dahmen on the occasion of his 60th birthday |
| topic | Dahmen, Wolfgang 1949- (DE-588)130554235 gnd Approximation - Aufsatzsammlung Numerische Mathematik - Aufsatzsammlung Numerische Mathematik (DE-588)4042805-9 gnd Approximation (DE-588)4002498-2 gnd |
| topic_facet | Dahmen, Wolfgang 1949- Approximation - Aufsatzsammlung Numerische Mathematik - Aufsatzsammlung Numerische Mathematik Approximation Aufsatzsammlung Bibliografie Festschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018653977&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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