Holdings: Quantitative approximations

Quantitative approximations:

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Bibliographic Details
Main Author:	Anastassiou, George A. 1952- (Author)
Format:	Book
Language:	English
Published:	Boca Raton, Fla. [u.a.] Chapman & Hall/CRC 2001
Subjects:	Approximation theory Numerical analysis Approximationstheorie
Online Access:	Inhaltsverzeichnis
Physical Description:	XIV, 607 S.
ISBN:	1584882212

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MARC


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Record in the Search Index

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adam_text	QUANTITATIVE APPROXIMATIONS GEORGE ANASTASSIOU DEPARTMENT OF MATHEMATICAL SCIENCES THE UNIVERSITY OF MEMPHIS MEMPHIS, TENNESSEE CHAPMAN & HALL/CRC . V, / , : J BOCA RATON LONDON NEW YORK WASHINGTON, D.C. - - * - CONTENTS PREFACE XIII 1 INTRODUCTION 1 1.1 ON CHAPTER 2: CONVERGENCE WITH RATES OF UNIVARIATE NEU- RAL NETWORK OPERATORS TO THE UNIT OPERATOR 1 1.2 ON CHAPTER 3: CONVERGENCE WITH RATES OF MULTIVARIATE NEURAL NETWORK OPERATORS TO THE UNIT OPERATOR 4 1.3 ON CHAPTER 4: ASYMPTOTIC WEAK CONVERGENCE OF CARDALIAGUET- EUVRARD NEURAL NETWORK OPERATORS 7 1.4 ON CHAPTER 5: ASYMPTOTIC WEAK CONVERGENCE OF SQUASHING NEURAL NETWORK OPERATORS 9 1.5 ON CHAPTER 6: QUANTITATIVE MONOTONE AND PROBABILISTIC WAVELET TYPE APPROXIMATION 10 1.6 ON CHAPTER 7: QUANTITATIVE ONE-DIMENSIONAL HIGH ORDER WAVELET TYPE APPROXIMATION 12 1.7 ON CHAPTER 8: MORE ON SHAPE AND PROBABILITY PRESERVING ONE-DIMENSIONAL WAVELET TYPE OPERATORS 14 1.8 ON CHAPTER 9: QUANTITATIVE MULTIDIMENSIONAL HIGH ORDER WAVELET TYPE APPROXIMATION 15 1.9 ON CHAPTER 10: RATE OF CONVERGENCE OF PROBABILISTIC DISCRETE WAVELET APPROXIMATION 18 1.10 ON CHAPTER 11: ASYMPTOTIC NONORTHOGONAL WAVELET APPROXIMATION FOR DETERMINISTIC SIGNALS 19 1.11 ON CHAPTER 12: WAVELET TYPE DIFFERENTIATED SHIFT INVARIANT INTEGRAL OPERATORS 20 1.12 ON CHAPTER 13: A DISCRETE KAC S FORMULA AND OPTIMAL QUANTITATIVE APPROXIMATION IN THE SOLUTION OF HEAT EQUATION 22 VLL VIII CONTENTS 1.13 ON CHAPTER 14: QUANTITATIVE-ASYMPTOTIC EXPANSIONS FOR THE PROBABILISTIC REPRESENTATION FORMULAE FOR (CO) M-PARAMETER OPERATOR SEMIGROUPS 25 1.14 ON CHAPTER 15: QUANTITATIVE PROBABILITY LIMIT THEOREMS OVER BANACH SPACES 27 1.15 ON CHAPTER 16: QUANTITATIVE STUDY OF BIAS CONVERGENCE FOR GENERALIZED L-STATISTICS 30 1.16 ON CHAPTER 17: QUANTITATIVE KOROVKIN-TYPE RESULTS FOR VECTOR VALUED FUNCTIONS 33 1.17 ON CHAPTER 18: QUANTITATIVE L P -RESULTS FOR POSITIVE LINEAR OPERATORS 35 1.18 ON CHAPTER 19: ON MONOTONE APPROXIMATION THEORY . . 38 1.19 ON CHAPTER 20: COMPARISONS FOR LOCAL MODULI OF CONTINUITY 41 1.20 ON CHAPTER 21: CONVERGENCE WITH RATES OF UNIVARIATE SINGULAR INTEGRALS TO THE UNIT 42 1.21 ON CHAPTER 22: ABOUT UNIVARIATE OSTROWSKI- TYPE INEQUALITIES 44 1.22 ON CHAPTER 23: ABOUT MULTIDIMENSIONAL OSTROWSKI-TYPE INEQUALITIES 45 1.23 ON CHAPTER 24: GENERAL OPIAL-TYPE INEQUALITIES FOR LINEAR DIFFERENTIAL OPERATORS 47 1.24 ON CHAPTER 25: L P -OPIAL INEQUALITIES ENGAGING FRACTIONAL DERIVATIVES OF FUNCTIONS 50 1.25 ON CHAPTER 26: L P -GENERAL FRACTIONAL OPIAL INEQUALITIES 52 1 ON NEURAL NETWORKS 57 2 CONVERGENCE WITH RATES OF UNIVARIATE NEURAL NETWORK OPERATORS TO THE UNIT OPERATOR 59 2.1 CONVERGENCE WITH RATES OF THE UNIVARIATE CARDALIAGUET-EUVRARD NEURAL NETWORK OPERATORS 60 2.2 THE UNIVARIATE SQUASHING OPERATORS AND THEIR CONVERGENCE TO THE UNIT WITH RATES 76 3 CONVERGENCE WITH RATES OF MULTIVARIATE NEURAL NETWORK OPERATORS TO THE UNIT OPERATOR 89 3.1 CONVERGENCE WITH RATES OF MULTIVARIATE CARDALIAGUET-EUVRARD NEURAL NETWORK OPERATORS 90 3.2 THE MULTIVARIATE SQUASHING OPERATORS AND THEIR CONVERGENCE TO THE UNIT WITH RATES ILL CONTENTS IX 4 ASYMPTOTIC WEAK CONVERGENCE OF CARDALIAGUET-EUVRARD NEURAL NETWORK OPERATORS 121 4.1 BACKGROUND 121 4.2 GENERAL RESULT 124 4.3 SUPPLEMENT 130 5 ASYMPTOTIC WEAK CONVERGENCE OF SQUASHING NEURAL NET- WORK OPERATORS 135 5.1 BACKGROUND 135 5.2 GENERAL RESULT 137 II ON WAVELETS 143 6 QUANTITATIVE MONOTONE AND PROBABILISTIC WAVELET TYPE APPROXIMATION 145 6.1 APPROXIMATION BY A K (F) OPERATORS 146 6.2 APPROXIMATION BY B K {F) OPERATORS 156 6.3 MORE RESULTS ON A K {F) AND B K {F) OPERATORS 159 7 QUANTITATIVE ONE-DIMENSIONAL HIGH ORDER WAVELET TYPE APPROXIMATION 165 7.1 ESTIMATES AND SHARPNESS 165 8 MORE ON SHAPE AND PROBABILITY PRESERVING ONE-DIMENSIONAL WAVELET TYPE OPERATORS 185 8.1 ESTIMATES, MAINTENANCE, AND SHARPNESS 186 9 QUANTITATIVE MULTIDIMENSIONAL HIGH ORDER WAVELET TYPE APPROXIMATION 201 9.1 ESTIMATES AND SHARPNESS 201 10 RATE OF CONVERGENCE OF PROBABILISTIC DISCRETE WAVELET APPROXIMATION 229 10.1 APPROXIMATION BY L K {F,X) OPERATORS 230 11 ASYMPTOTIC NONORTHOGONAL WAVELET APPROXIMATION FOR DETERMINISTIC SIGNALS 235 11.1 INTRODUCTION 235 11.2 ASYMPTOTIC WAVELET APPROXIMATION AT RESOLUTION 2~ FC . . 237 12 WAVELET TYPE DIFFERENTIATED SHIFT-INVARIANT INTEGRAL OPERATORS 259 12.1 GENERAL RESULTS 259 12.2 EXAMPLES 269 CONTENTS III ON PARTIAL DIFFERENTIAL EQUATIONS 273 13 A DISCRETE KAC S FORMULA AND OPTIMAL QUANTITATIVE APPROXIMATION IN THE SOLUTION OF HEAT EQUATION 275 13.1 AUXILIARY RESULTS 277 13.2 THE DIRICHLET PROBLEM: DISCRETE CASE 279 13.3 ABOUT APPROXIMATION ON THE GRID 293 13.4 ON SHARPNESS OF THE ERROR ESTIMATE 299 IV ON SEMIGROUPS 303 14 QUANTITATIVE ASYMPTOTIC EXPANSIONS OF THE PROBABILISTIC REPRESENTATION FORMULAE FOR (CO) M-PARAMETER OPERATOR SEMIGROUPS 305 14.1 BACKGROUND 305 14.2 BASIC RESULTS 308 14.3 QUANTITATIVE ASYMPTOTIC PROBABILISTIC EXPANSIONS 314 14.4 ASYMPTOTIC PROBABILISTIC EXPANSIONS FOR CONTINUOUS TYPE FORMULAE 323 14.5 EXAMPLES 327 V ON STOCHASTICS 333 15 QUANTITATIVE PROBABILITY LIMIT THEOREMS OVER BANACH SPACES 335 15.1 LIMIT THEOREMS FOR MARTINGALES IN BANACH SPACES 336 15.1.1 AUXILIARY RESULTS 336 15.1.2 MAIN THEOREMS 340 15.2 ON WEAK INVARIANCE PRINCIPLE 348 15.2.1 BACKGROUND 348 15.2.2 CENTRAL RESULTS 352 16 QUANTITATIVE STUDY OF BIAS CONVERGENCE FOR GENERALIZED L-STATISTICS 361 16.1 BACKGROUND 361 16.2 QUANTITATIVE RESULTS FOR L-STATISTICS WITH STANDARD WEIGHTS 365 16.3 QUANTITATIVE RESULTS FOR L-STATISTICS WITH NONSTANDARD WEIGHTS 369 16.4 MORE CONCLUSIONS 379 CONTENTS XI VI ON FUNCTIONAL ANALYSIS 381 17 QUANTITATIVE KOROVKIN-TYPE RESULTS FOR VECTOR VALUED FUNCTIONS 383 17.1 BACKGROUND 383 17.2 AUXILIARY RESULTS 385 17.3 QUANTITATIVE GENERAL THEOREMS 396 17.4 FURTHER RESULTS 405 17.5 APPLICATIONS 411 18 QUANTITATIVE L P -RESULTS FOR POSITIVE LINEAR OPERATORS 413 18.1 BACKGROUND 414 18.2 UNIVARIATE RESULTS 419 18.3 ABSTRACT THEORY 433 18.4 MULTIDIMENSIONAL THEORY 438 18.5 STOCHASTIC THEORY 444 VII ON APPROXIMATION THEORY 449 19 ON MONOTONE APPROXIMATION THEORY 451 19.1 HIGH ORDER QUANTITATIVE MONOTONE APPROXIMATION WITH LINEAR DIFFERENTIAL OPERATORS 451 19.2 QUANTITATIVE MONOTONE APPROXIMATION WITH PSEUDO-POLYNOMIALS 455 19.3 QUANTITATIVE BIVARIATE MONOTONE APPROXIMATION 461 19.4 QUANTITATIVE SPLINE MONOTONE APPROXIMATION WITH LINEAR DIFFERENTIAL OPERATORS 465 19.4.1 QUANTITATIVE MONOTONE APPROXIMATION BY POLYNOMIAL SPLINES 465 19.4.2 QUANTITATIVE MONOTONE APPROXIMATION BY PERIODIC POLYNOMIAL SPLINES 469 19.4.3 QUANTITATIVE MONOTONE APPROXIMATION BY DISCRETE POLYNOMIAL SPLINES 471 20 COMPARISONS FOR LOCAL MODULI OF CONTINUITY 473 20.1 UNIVARIATE RESULTS 473 20.2 A MULTIVARIATE RESULT 479 21 CONVERGENCE WITH RATES OF UNIVARIATE SINGULAR INTEGRALS TO THE UNIT 483 21.1 BACKGROUND 483 21.2 QUANTITATIVE L P - APPROXIMATION, 1 P +OO 485 XII CONTENTS 21.3 QUANTITATIVE UNIFORM APPROXIMATION BY Q N ^ OPERATOR 492 VIII ON CLASSICAL ANALYSIS 495 22 ABOUT UNIVARIATE OSTROWSKI-TYPE INEQUALITIES 497 22.1 ABOUT OSTROWSKI S INEQUALITY 497 22.2 ABOUT MORE GENERAL UNIVARIATE OSTROWSKI-TYPE INEQUALITIES 499 23 ABOUT MULTIDIMENSIONAL OSTROWSKI-TYPE INEQUALITIES 507 23.1 GENERAL RESULTS 507 24 GENERAL OPIAL-TYPE INEQUALITIES FOR LINEAR DIFFERENTIAL OPERATORS 521 24.1 SETTING . - 522 24.2 GENERAL RESULTS 523 24.3 AN APPLICATION TO DIFFERENTIAL EQUATIONS 536 25 LP-OPIAL-TYPE INEQUALITIES ENGAGING FRACTIONAL DERIVATIVES OF FUNCTIONS 539 25.1 BACKGROUND 539 25.2 GENERAL RESULTS 545 25.3 APPLICATIONS TO DIFFERENTIAL EQUATIONS 556 26 I P -GENERAL FRACTIONAL OPIAL INEQUALITIES 567 26.1 GENERAL RESULTS 567 REFERENCES 585 LIST OF SYMBOLS 599 INDEX 605
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spelling	Anastassiou, George A. 1952- Verfasser (DE-588)121815900 aut Quantitative approximations George Anastassiou Boca Raton, Fla. [u.a.] Chapman & Hall/CRC 2001 XIV, 607 S. txt rdacontent n rdamedia nc rdacarrier Approximation theory Numerical analysis Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Approximationstheorie (DE-588)4120913-8 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009478735&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Anastassiou, George A. 1952- Quantitative approximations Approximation theory Numerical analysis Approximationstheorie (DE-588)4120913-8 gnd
subject_GND	(DE-588)4120913-8
title	Quantitative approximations
title_auth	Quantitative approximations
title_exact_search	Quantitative approximations
title_full	Quantitative approximations George Anastassiou
title_fullStr	Quantitative approximations George Anastassiou
title_full_unstemmed	Quantitative approximations George Anastassiou
title_short	Quantitative approximations
title_sort	quantitative approximations
topic	Approximation theory Numerical analysis Approximationstheorie (DE-588)4120913-8 gnd
topic_facet	Approximation theory Numerical analysis Approximationstheorie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009478735&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT anastassiougeorgea quantitativeapproximations

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