Intelligent Mathematics: computational analysis
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2011
|
| Series: | Intelligent Systems Reference Library
5 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XVII, 802 S. |
| ISBN: | 9783642170973 3642170978 |
Staff View
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Record in the Search Index
| _version_ | 1805096344035000320 |
|---|---|
| adam_text |
IMAGE 1
CONTENTS
1 I N T R O D U C T I ON 1
2 C O N V EX P R O B A B I L I S T IC WAVELET LIKE A P P R O X I M A T I
ON 13
2.1 INTRODUCTION 13
2.2 CONVEX WAVELET LIKE APPROXIMATION 14
2.3 R-TLI CONVEX WAVELET APPROXIMATION 20
2.4 COCONVEX PROBABILISTIC WAVELET LIKE APPROXIMATION 2G
3 B I D I M E N S I O N AL C O N S T R A I N ED W A V E L ET LIKE A P P
R O X I M A T I ON 29
3.1 INTRODUCTION 29
3.2 RESULTS 30
4 M U L T I D I M E N S I O N AL P R O B A B I L I S T IC SCALE A P P R
O X I M A T I ON 41
4.1 INTRODUCTION 41
4.2 MAIN RESULT 42
5 M U L T I D I M E N S I O N AL PROBABILISTIC A P P R O X I M A T I ON
IN W A V E L ET LIKE S T R U C T U RE 57
5.1 INTRODUCTION 57
5.2 RESULTS 58
6 A B O UT L - P O S I T I VE A P P R O X I M A T I O NS G9
G.L INTRODUCTION 09
0.2 L-POSITIVE APPROXIMATION IN A NORMED SPACE 71
0.3 L-POSITIVE APPROXIMATION IN FUNCTIONAL SPACES 73
0.4 MULTIDIMENSIONAL JACKSON TYPE THEOREMS FOR SIMULTANEOUS
APPROXIMATION 78
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1007492570
DIGITALISIERT DURCH
IMAGE 2
XII CONTENTS
7 ABOUT SHAPE PRESERVING WEIGHTED UNIFORM APPROXIMATION 89
7.1 INTRODUCTION 89
7.2 SHAPE PRESERVING WEIGHTED UNIFORM APPROXIMATION 89
8 JACKSON-TYPE NONPOSITIVE APPROXIMATIONS FOR DEFINITE INTEGRALS 93
8.1 INTRODUCTION 93
8.2 MAIN RESULTS 94
9 DISCRETE BEST L\ APPROXIMATION USING THE GAUGES WAY 99
9.1 INTRODUCTION 99
9.2 BACKGROUND 100
9.3 MORE BACKGROUND 101
9.4 BASIC RESULT 102
9.5 MAIN RESULT 103
9.6 PREPARATION RESULTS 104
9.7 ANOTHER MAIN RESULT 105
9.8 CONCLUSIONS 109
9.9 PROOFS 109
9.10 MORE PROOFS 110
9.11 FINAL CONCLUSIONS 112
10 QUANTITATIVE UNIFORM CONVERGENCE OF SMOOTH PICARD SINGULAR INTEGRAL
OPERATORS 115
10.1 INTRODUCTION 115
10.2 RESULTS 116
11 GLOBAL SMOOTHNESS AND SIMULTANEOUS APPROXIMATION BY SMOOTH PICARD
SINGULAR OPERATORS 137
11.1 INTRODUCTION 137
11.2 GLOBAL SMOOTHNESS PRESERVATION RESULTS 138
11.3 CONVERGENCE RESULTS 143
12 QUANTITATIVE L P APPROXIMATION BY SMOOTH PICARD SINGULAR OPERATORS
151
12.1 INTRODUCTION 151
12.2 RESULTS 152
13 APPROXIMATION WITH RATES BY FRACTIONAL SMOOTH PICARD SINGULAR
OPERATORS 109
13.1 BACKGROUND 169
13.2 MAIN RESULTS 177
13.3 APPLICATIONS 188
IMAGE 3
CONTENTS XIII
14 MULTIVARIATE GENERALIZED PICARD SINGULAR INTEGRAL OPERATORS 191
14.1 BACKGROUND 191
14.2 CONSTRUCTION OF A FAMILY OF SINGULAR INTEGRAL OPERATORS . . . 194
14.3 APPROXIMATION PROPERTIES OF THE OPERATOR P\,/3 (/; *) 196 14.4
GLOBAL SMOOTHNESS PRESERVATION PROPERTY 203
15 APPROXIMATION BY Q-GAUSS-WEIERSTRASS SINGULAR INTEGRAL OPERATORS 207
15.1 INTRODUCTION 207
15.2 DESCRIPTION OF THE OPERATORS 209
15.3 APPROXIMATION PROPERTIES IN A WEIGHTED SPACE 210
16 QUANTITATIVE APPROXIMATION BY UNIVARIATE SHIFT-INVARIANT INTEGRAL
OPERATORS 215
16.1 BACKGROUND 215
16.2 MAIN RESULTS 217
16.3 APPLICATIONS 230
17 QUANTITATIVE APPROXIMATION BY MULTIVARIATE SHIFT-INVARIANT
CONVOLUTION OPERATORS 239
17.1 BACKGROUND 239
17.2 MAIN RESULTS 241
18 APPROXIMATION BY A NONLINEAR CARDALIAGUET-EUVRARD NEURAL NETWORK
OPERATOR OF MAX-PRODUCT KIND 201 18.1 INTRODUCTION 201
18.2 AUXILIARY RESULTS 203
18.3 APPROXIMATION RESULTS 205
18.4 CONCLUSION 271
19 A GENERALIZED SHISHA - MOND TYPE INEQUALITY 273
19.1 RESULTS 273
20 QUANTITATIVE APPROXIMATION BY BOUNDED LINEAR OPERATORS 275
20.1 INTRODUCTION 275
20.2 RESULTS 276
21 QUANTITATIVE STOCHASTIC KOROVKIN THEORY 281
21.1 INTRODUCTION 281
21.2 MAIN RESULTS 282
IMAGE 4
XIV CONTENTS
22 QUANTITATIVE MULTIDIMENSIONAL STOCHASTIC KOROVKIN THEORY 299
22.1 INTRODUCTION 299
22.2 BACKGROUND 300
22.3 MAIN RESULTS 303
23 ABOUT THE RIGHT FRACTIONAL CALCULUS 333
23.1 ABOUT THE RIGHT CAPUTO FRACTIONAL DERIVATIVE 333
23.2 ABOUT THE RIGHT GENERALIZED FRACTIONAL DERIVATIVE 345 23.3 ABOUT
THE RIGHT AND LEFT WEYL FRACTIONAL DERIVATIVES 348 23.4 CONSEQUENCES 352
24 FRACTIONAL CONVERGENCE THEORY OF POSITIVE LINEAR OPERATORS 355
24.1 INTRODUCTION 355
24.2 BACKGROUND 358
24.3 MAIN RESULTS 360
24.4 APPLICATION 373
25 FRACTIONAL TRIGONOMETRIE CONVERGENCE THEORY OF POSITIVE LINEAR
OPERATORS 377
25.1 INTRODUCTION 377
25.2 BACKGROUND 379
25.3 MAIN RESULTS 385
25.4 APPLICATION 394
26 EXTENDED INTEGRAL INEQUALITIES 399
26.1 INTRODUCTION 399
26.2 RESULTS 400
27 BALANCED FRACTIONAL OPIAL INTEGRAL INEQUALITIES 423
27.1 BACKGROUND 423
27.2 RESULTS 420
28 MONTGOMERY IDENTITIES FOR FRACTIONAL INTEGRALS AND FRACTIONAL
INEQUALITIES 435
28.1 INTRODUCTION 435
28.2 FRACTIONAL CALCULUS 436
28.3 MONTGOMERY IDENTITIES FOR FRACTIONAL INTEGRALS 437 28.4 AN
OSTROWSKI TYPE FRACTIONAL INEQUALITY 440
28.5 A GRUESS TYPE FRACTIONAL INEQUALITY 441
29 REPRESENTATIONS FOR (CO) M-PARAMETER OPERATOR SEMIGROUPS 443
29.1 HISTORY 443
29.2 BACKGROUND 444
IMAGE 5
CONTENTS XV
29.3 BASIC RESULTS 440
29.4 MAIN RESULTS 451
29.5 FURTHER RESULTS: MULTIPLIER ENLARGEMENT FORMULAE 458 29.6
APPLICATIONS 461
30 SIMULTANEOUS APPROXIMATION USING THE FEILER PROBABILISTIC OPERATOR
469
30.1 BASICS 409
30.2 THE MAIN RESULT 470
30.3 PROOF OF THEOREM 30.1 471
30.4 APPLICATIONS 481
31 GLOBAL SMOOTHNESS PRESERVATION AND UNIFORM CONVERGENCE OF SINGULAR
INTEGRAL OPERATORS IN THE FUZZY SENSE 487
31.1 FUZZY REAL ANALYSIS BACKGROUND 487
31.2 MAIN RESULTS 492
32 REAL APPROXIMATIONS TRANSFERRED TO VECTORIAL AND FUZZY SETTING 503
32.1 RESULTS 503
33 HIGH ORDER MULTIVARIATE APPROXIMATION BY MULTIVARIATE WAVELET TYPE
AND NEURAL NETWORK OPERATORS IN THE FUZZY SENSE 523
33.1 FUZZY REAL ANALYSIS BACKGROUND 523
33.2 MAIN RESULTS 529
33.2.1 CONVERGENCE WITH RATES OF MULTIVARIATE FUZZY WAVELET TYPE
OPERATORS 529
33.2.2 CONVERGENCE WITH RATES OF MULTIVARIATE FUZZY CARDALIAGUET-
EUVRARD NEURAL NETWORK OPERATORS . . 542 33.2.3 THE MULTIVARIATE FUZZY
"SQUASHING OPERATORS" AND THEIR FUZZY CONVERGENCE TO THE UNIT WITH
RATES 549
34 FUZZY FRACTIONAL CALCULUS AND THE OSTROWSKI INTEGRAL INEQUALITY 553
34.1 FUZZY MATHEMATICAL ANALYSIS BACKGROUND 553
34.2 MAIN RESULTS 501
35 ABOUT DISCRETE FRACTIONAL CALCULUS WITH INEQUALITIES . . . 575 35.1
BACKGROUND 575
35.2 RESULTS 577
IMAGE 6
XVI CONTENTS
36 DISCRETE NABLA FRACTIONAL CALCULUS WITH INEQUALITIES 587 30.1
BACKGROUND 587
36.2 MAIN RESULTS 589
37 ABOUT Q- INEQUALITIES 601
37.1 INTRODUCTION 001
37.2 MAIN RESULTS 605
38 ABOUT Q- FRACTIONAL INEQUALITIES 615
38.1 BACKGROUND 615
38.2 MAIN RESULTS 618
39 INEQUALITIES ON TIME SCALES 627
39.1 BACKGROUND 627
39.2 MAIN RESULTS 631
39.3 APPLICATIONS 640
40 NABLA INEQUALITIES ON TIME SCALES 649
40.1 PRELIMINARIES 649
40.2 MAIN RESULTS 656
40.3 APPLICATIONS 665
41 THE PRINCIPIE OF DUALITY IN TIME SCALES WITH INEQUALITIES 673
41.1 PRELIMINARIES 673
41.2 THE DUAL TIME SCALE 675
41.3 DUAL CORRESPONDENCES 675
41.4 DUAL GENERALIZED MONOMIALS 678
41.5 TIME SCALES INTEGRAL INEQUALITIES 680
41.6 APPLICATIONS 690
42 FOUNDATIONS OF DELTA FRACTIONAL CALCULUS ON TIME SCALES WITH
INEQUALITIES 695
42.1 BACKGROUND AND FOUNDATION RESULTS 695
42.2 FRACTIONAL DELTA INEQUALITIES ON TIME SCALES 702
42.3 APPLICATIONS 708
43 PRINCIPLES OF NABLA FRACTIONAL CALCULUS ON TIME SCALES WITH
INEQUALITIES 711
43.1 BACKGROUND AND FOUNDATION RESULTS 711
43.2 FRACTIONAL NABLA INEQUALITIES ON TIME SCALES 719
43.3 APPLICATIONS 725
IMAGE 7
CONTENTS XVII
44 OPTIMAL ERROR ESTIMATE FOR THE NUMERICAL SOLUTION OF MULTIDIMENSIONAL
DIRICHLET PROBLEM 731
44.1 INTRODUCTION 731
44.2 BACKGROUND 732
44.2.1 DIRICHLET PROBLEM: CONTINUOUS CASE 732
44.2.2 DIRICHLET PROBLEM: DISCRETE CASE 735
44.3 MAIN RESULTS 741
44.3.1 APPROXIMATION ON THE UNIFORM GRID 741
44.3.2 SHARPNESS OF THE ERROR ESTIMATES FOR A DIRICHLET PROBLEM 744
44.3.3 REMARKS CONCERNING THE CASE OF A GENERAL DOMAIN Q C R' 747
45 OPTIMAL ESTIMATE FOR THE NUMERICAL SOLUTION OF MULTIDIMENSIONAL
DIRICHLET PROBLEM FOR THE HEAT EQUATION 749
45.1 DESCRIPTION 749
45.2 BASICS 750
45.3 DIRICHLET PROBLEM: DISCRETE CASE 754
45.4 APPROXIMATION OVER THE GRID 759
45.5 SHARPNESS FOR THE ERROR ESTIMATES OF THE DIRICHLET PROBLEM FOR THE
HEAT EQUATION 763
46 UNIQUENESS OF SOLUTION IN EVOLUTION IN MULTIVARIATE TIME 705
46.1 INTRODUCTION 765
46.2 BIVARIATE TIME 765
40.3 THE UNIQUENESS THEOREM 766
46.4 PROOF OF THEOREM 46.2 708
46.5 HISTORY, MOTIVATION AND RELATED RESULTS 770
46.6 EXAMPLES 772
REFERENCES 773
LIST OF SYMBOLS 791
INDEX 797 |
| any_adam_object | 1 |
| author | Anastassiou, George A. 1952- |
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| author_facet | Anastassiou, George A. 1952- |
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| dewey-full | 518 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518 |
| dewey-search | 518 |
| dewey-sort | 3518 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV039120591 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T11:13:40Z |
| institution | BVB |
| isbn | 9783642170973 3642170978 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024139186 |
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| owner_facet | DE-83 DE-91 DE-BY-TUM |
| physical | XVII, 802 S. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Springer |
| record_format | marc |
| series | Intelligent Systems Reference Library |
| series2 | Intelligent Systems Reference Library |
| spelling | Anastassiou, George A. 1952- Verfasser (DE-588)121815900 aut Intelligent Mathematics computational analysis George A. Anastassiou Berlin [u.a.] Springer 2011 XVII, 802 S. txt rdacontent n rdamedia nc rdacarrier Intelligent Systems Reference Library 5 Approximation (DE-588)4002498-2 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 s DE-604 Approximation (DE-588)4002498-2 s Intelligent Systems Reference Library 5 (DE-604)BV035704685 5 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3547130&prov=M&dok%5Fvar=1&dok%5Fext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024139186&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Anastassiou, George A. 1952- Intelligent Mathematics computational analysis Intelligent Systems Reference Library Approximation (DE-588)4002498-2 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4002498-2 (DE-588)4042805-9 |
| title | Intelligent Mathematics computational analysis |
| title_auth | Intelligent Mathematics computational analysis |
| title_exact_search | Intelligent Mathematics computational analysis |
| title_full | Intelligent Mathematics computational analysis George A. Anastassiou |
| title_fullStr | Intelligent Mathematics computational analysis George A. Anastassiou |
| title_full_unstemmed | Intelligent Mathematics computational analysis George A. Anastassiou |
| title_short | Intelligent Mathematics |
| title_sort | intelligent mathematics computational analysis |
| title_sub | computational analysis |
| topic | Approximation (DE-588)4002498-2 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Approximation Numerische Mathematik |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3547130&prov=M&dok%5Fvar=1&dok%5Fext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024139186&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035704685 |
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