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Error estimation for pattern recognition / / Ulisses M. Braga Neto, Edward R. Dougherty
| Error estimation for pattern recognition / / Ulisses M. Braga Neto, Edward R. Dougherty |
| Autore | Braga-Neto Ulisses de Mendon AÀca |
| Pubbl/distr/stampa | Chichester, West Sussex : , : Wiley Blackwell, , 2015 |
| Descrizione fisica | 1 online resource (336 p.) |
| Disciplina | 610.28 |
| Collana | IEEE press series on biomedical engineering |
| Soggetto topico |
Biomedical engineering -- Congresses
Image processing -- Digital techniques Optical pattern recognition Pattern recognition systems - Mathematics Pattern perception Error analysis (Mathematics) Electrical Engineering Electrical & Computer Engineering Engineering & Applied Sciences |
| ISBN |
1-119-07937-3
1-119-07933-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | PREFACE XIII -- ACKNOWLEDGMENTS XIX -- LIST OF SYMBOLS XXI -- 1 CLASSIFICATION 1 -- 1.1 Classifiers 1 -- 1.2 Population-Based Discriminants 3 -- 1.3 Classification Rules 8 -- 1.4 Sample-Based Discriminants 13 -- 1.4.1 Quadratic Discriminants 14 -- 1.4.2 Linear Discriminants 15 -- 1.4.3 Kernel Discriminants 16 -- 1.5 Histogram Rule 16 -- 1.6 Other Classification Rules 20 -- 1.6.1 k-Nearest-Neighbor Rules 20 -- 1.6.2 Support Vector Machines 21 -- 1.6.3 Neural Networks 22 -- 1.6.4 Classification Trees 23 -- 1.6.5 Rank-Based Rules 24 -- 1.7 Feature Selection 25 -- Exercises 28 -- 2 ERROR ESTIMATION35 -- 2.1 Error Estimation Rules 35 -- 2.2 Performance Metrics 38 -- 2.2.1 Deviation Distribution 39 -- 2.2.2 Consistency 41 -- 2.2.3 Conditional Expectation 41 -- 2.2.4 Linear Regression 42 -- 2.2.5 Confidence Intervals 42 -- 2.3 Test-Set Error Estimation 43 -- 2.4 Resubstitution 46 -- 2.5 Cross-Validation 48 -- 2.6 Bootstrap 55 -- 2.7 Convex Error Estimation 57 -- 2.8 Smoothed Error Estimation 61 -- 2.9 Bolstered Error Estimation 63 -- 2.9.1 Gaussian-Bolstered Error Estimation 67 -- 2.9.2 Choosing the Amount of Bolstering 68 -- 2.9.3 Calibrating the Amount of Bolstering 71 -- Exercises 73 -- 3 PERFORMANCE ANALYSIS77 -- 3.1 Empirical Deviation Distribution 77 -- 3.2 Regression 79 -- 3.3 Impact on Feature Selection 82 -- 3.4 Multiple-Data-Set Reporting Bias 84 -- 3.5 Multiple-Rule Bias 86 -- 3.6 Performance Reproducibility 92 -- Exercises 94 -- 4 ERROR ESTIMATION FOR DISCRETE CLASSIFICATION 97 -- 4.1 Error Estimators 98 -- 4.1.1 Resubstitution Error 98 -- 4.1.2 Leave-One-Out Error 98 -- 4.1.3 Cross-Validation Error 99 -- 4.1.4 Bootstrap Error 99 -- 4.2 Small-Sample Performance 101 -- 4.2.1 Bias 101 -- 4.2.2 Variance 103 -- 4.2.3 Deviation Variance, RMS, and Correlation 105 -- 4.2.4 Numerical Example 106 -- 4.2.5 Complete Enumeration Approach 108 -- 4.3 Large-Sample Performance 110 -- Exercises 114 -- 5 DISTRIBUTION THEORY 115 -- 5.1 Mixture Sampling Versus Separate Sampling 115 -- 5.2 Sample-Based Discriminants Revisited 119 -- 5.3 True Error 120 -- 5.4 Error Estimators 121 -- 5.4.1 Resubstitution Error 121 -- 5.4.2 Leave-One-Out Error 122 -- 5.4.3 Cross-Validation Error 122 -- 5.4.4 Bootstrap Error 124 -- 5.5 Expected Error Rates 125 -- 5.5.1 True Error 125 -- 5.5.2 Resubstitution Error 128 -- 5.5.3 Leave-One-Out Error 130 -- 5.5.4 Cross-Validation Error 132 -- 5.5.5 Bootstrap Error 133 -- 5.6 Higher-Order Moments of Error Rates 136 -- 5.6.1 True Error 136 -- 5.6.2 Resubstitution Error 137 -- 5.6.3 Leave-One-Out Error 139 -- 5.7 Sampling Distribution of Error Rates 140 -- 5.7.1 Resubstitution Error 140 -- 5.7.2 Leave-One-Out Error 141 -- Exercises 142 -- 6 GAUSSIAN DISTRIBUTION THEORY: UNIVARIATE CASE 145 -- 6.1 Historical Remarks 146 -- 6.2 Univariate Discriminant 147 -- 6.3 Expected Error Rates 148 -- 6.3.1 True Error 148 -- 6.3.2 Resubstitution Error 151 -- 6.3.3 Leave-One-Out Error 152 -- 6.3.4 Bootstrap Error 152 -- 6.4 Higher-Order Moments of Error Rates 154 -- 6.4.1 True Error 154 -- 6.4.2 Resubstitution Error 157 -- 6.4.3 Leave-One-Out Error 160 -- 6.4.4 Numerical Example 165 -- 6.5 Sampling Distributions of Error Rates 166 -- 6.5.1 Marginal Distribution of Resubstitution Error 166 -- 6.5.2 Marginal Distribution of Leave-One-Out Error 169 -- 6.5.3 Joint Distribution of Estimated and True Errors 174 -- Exercises 176 -- 7 GAUSSIAN DISTRIBUTION THEORY: MULTIVARIATE CASE 179 -- 7.1 Multivariate Discriminants 179 -- 7.2 Small-Sample Methods 180 -- 7.2.1 Statistical Representations 181 -- 7.2.2 Computational Methods 194 -- 7.3 Large-Sample Methods 199 -- 7.3.1 Expected Error Rates 200 -- 7.3.2 Second-Order Moments of Error Rates 207 -- Exercises 218 -- 8 BAYESIAN MMSE ERROR ESTIMATION221 -- 8.1 The Bayesian MMSE Error Estimator 222 -- 8.2 Sample-Conditioned MSE 226 -- 8.3 Discrete Classification 227 -- 8.4 Linear Classification of Gaussian Distributions 238 -- 8.5 Consistency 246 -- 8.6 Calibration 253 -- 8.7 Concluding Remarks 255 -- Exercises 257 -- A BASIC PROBABILITY REVIEW 259 -- A.1 Sample Spaces and Events 259 -- A.2 Definition of Probability 260 -- A.3 Borel-Cantelli Lemmas 261 -- A.4 Conditional Probability 262 -- A.5 Random Variables 263 -- A.6 Discrete Random Variables 265 -- A.7 Expectation 266 -- A.8 Conditional Expectation 268 -- A.9 Variance 269 -- A.10 Vector Random Variables 270 -- A.11 The Multivariate Gaussian 271 -- A.12 Convergence of Random Sequences 273 -- A.13 Limiting Theorems 275 -- B VAPNIK-CHERVONENKIS THEORY 277 -- B.1 Shatter Coefficients 277 -- B.2 The VC Dimension 278 -- B.3 VC Theory of Classification 279 -- B.3.1 Linear Classification Rules 279 -- B.3.2 kNN Classification Rule 280 -- B.3.3 Classification Trees 280 -- B.3.4 Nonlinear SVMs 281 -- B.3.5 Neural Networks 281 -- B.3.6 Histogram Rules 281 -- B.4 Vapnik-Chervonenkis Theorem 282 -- C DOUBLE ASYMPTOTICS 285 -- BIBLIOGRAPHY 291 -- AUTHOR INDEX 301 -- SUBJECT INDEX 305. |
| Record Nr. | UNINA-9910131376903321 |
Braga-Neto Ulisses de Mendon AÀca
|
||
| Chichester, West Sussex : , : Wiley Blackwell, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Error estimation for pattern recognition / / Ulisses M. Braga Neto, Edward R. Dougherty
| Error estimation for pattern recognition / / Ulisses M. Braga Neto, Edward R. Dougherty |
| Autore | Braga-Neto Ulisses de Mendon AÀca |
| Pubbl/distr/stampa | Chichester, West Sussex : , : Wiley Blackwell, , 2015 |
| Descrizione fisica | 1 online resource (336 p.) |
| Disciplina | 610.28 |
| Collana | IEEE press series on biomedical engineering |
| Soggetto topico |
Biomedical engineering -- Congresses
Image processing -- Digital techniques Optical pattern recognition Pattern recognition systems - Mathematics Pattern perception Error analysis (Mathematics) Electrical Engineering Electrical & Computer Engineering Engineering & Applied Sciences |
| ISBN |
1-119-07937-3
1-119-07933-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | PREFACE XIII -- ACKNOWLEDGMENTS XIX -- LIST OF SYMBOLS XXI -- 1 CLASSIFICATION 1 -- 1.1 Classifiers 1 -- 1.2 Population-Based Discriminants 3 -- 1.3 Classification Rules 8 -- 1.4 Sample-Based Discriminants 13 -- 1.4.1 Quadratic Discriminants 14 -- 1.4.2 Linear Discriminants 15 -- 1.4.3 Kernel Discriminants 16 -- 1.5 Histogram Rule 16 -- 1.6 Other Classification Rules 20 -- 1.6.1 k-Nearest-Neighbor Rules 20 -- 1.6.2 Support Vector Machines 21 -- 1.6.3 Neural Networks 22 -- 1.6.4 Classification Trees 23 -- 1.6.5 Rank-Based Rules 24 -- 1.7 Feature Selection 25 -- Exercises 28 -- 2 ERROR ESTIMATION35 -- 2.1 Error Estimation Rules 35 -- 2.2 Performance Metrics 38 -- 2.2.1 Deviation Distribution 39 -- 2.2.2 Consistency 41 -- 2.2.3 Conditional Expectation 41 -- 2.2.4 Linear Regression 42 -- 2.2.5 Confidence Intervals 42 -- 2.3 Test-Set Error Estimation 43 -- 2.4 Resubstitution 46 -- 2.5 Cross-Validation 48 -- 2.6 Bootstrap 55 -- 2.7 Convex Error Estimation 57 -- 2.8 Smoothed Error Estimation 61 -- 2.9 Bolstered Error Estimation 63 -- 2.9.1 Gaussian-Bolstered Error Estimation 67 -- 2.9.2 Choosing the Amount of Bolstering 68 -- 2.9.3 Calibrating the Amount of Bolstering 71 -- Exercises 73 -- 3 PERFORMANCE ANALYSIS77 -- 3.1 Empirical Deviation Distribution 77 -- 3.2 Regression 79 -- 3.3 Impact on Feature Selection 82 -- 3.4 Multiple-Data-Set Reporting Bias 84 -- 3.5 Multiple-Rule Bias 86 -- 3.6 Performance Reproducibility 92 -- Exercises 94 -- 4 ERROR ESTIMATION FOR DISCRETE CLASSIFICATION 97 -- 4.1 Error Estimators 98 -- 4.1.1 Resubstitution Error 98 -- 4.1.2 Leave-One-Out Error 98 -- 4.1.3 Cross-Validation Error 99 -- 4.1.4 Bootstrap Error 99 -- 4.2 Small-Sample Performance 101 -- 4.2.1 Bias 101 -- 4.2.2 Variance 103 -- 4.2.3 Deviation Variance, RMS, and Correlation 105 -- 4.2.4 Numerical Example 106 -- 4.2.5 Complete Enumeration Approach 108 -- 4.3 Large-Sample Performance 110 -- Exercises 114 -- 5 DISTRIBUTION THEORY 115 -- 5.1 Mixture Sampling Versus Separate Sampling 115 -- 5.2 Sample-Based Discriminants Revisited 119 -- 5.3 True Error 120 -- 5.4 Error Estimators 121 -- 5.4.1 Resubstitution Error 121 -- 5.4.2 Leave-One-Out Error 122 -- 5.4.3 Cross-Validation Error 122 -- 5.4.4 Bootstrap Error 124 -- 5.5 Expected Error Rates 125 -- 5.5.1 True Error 125 -- 5.5.2 Resubstitution Error 128 -- 5.5.3 Leave-One-Out Error 130 -- 5.5.4 Cross-Validation Error 132 -- 5.5.5 Bootstrap Error 133 -- 5.6 Higher-Order Moments of Error Rates 136 -- 5.6.1 True Error 136 -- 5.6.2 Resubstitution Error 137 -- 5.6.3 Leave-One-Out Error 139 -- 5.7 Sampling Distribution of Error Rates 140 -- 5.7.1 Resubstitution Error 140 -- 5.7.2 Leave-One-Out Error 141 -- Exercises 142 -- 6 GAUSSIAN DISTRIBUTION THEORY: UNIVARIATE CASE 145 -- 6.1 Historical Remarks 146 -- 6.2 Univariate Discriminant 147 -- 6.3 Expected Error Rates 148 -- 6.3.1 True Error 148 -- 6.3.2 Resubstitution Error 151 -- 6.3.3 Leave-One-Out Error 152 -- 6.3.4 Bootstrap Error 152 -- 6.4 Higher-Order Moments of Error Rates 154 -- 6.4.1 True Error 154 -- 6.4.2 Resubstitution Error 157 -- 6.4.3 Leave-One-Out Error 160 -- 6.4.4 Numerical Example 165 -- 6.5 Sampling Distributions of Error Rates 166 -- 6.5.1 Marginal Distribution of Resubstitution Error 166 -- 6.5.2 Marginal Distribution of Leave-One-Out Error 169 -- 6.5.3 Joint Distribution of Estimated and True Errors 174 -- Exercises 176 -- 7 GAUSSIAN DISTRIBUTION THEORY: MULTIVARIATE CASE 179 -- 7.1 Multivariate Discriminants 179 -- 7.2 Small-Sample Methods 180 -- 7.2.1 Statistical Representations 181 -- 7.2.2 Computational Methods 194 -- 7.3 Large-Sample Methods 199 -- 7.3.1 Expected Error Rates 200 -- 7.3.2 Second-Order Moments of Error Rates 207 -- Exercises 218 -- 8 BAYESIAN MMSE ERROR ESTIMATION221 -- 8.1 The Bayesian MMSE Error Estimator 222 -- 8.2 Sample-Conditioned MSE 226 -- 8.3 Discrete Classification 227 -- 8.4 Linear Classification of Gaussian Distributions 238 -- 8.5 Consistency 246 -- 8.6 Calibration 253 -- 8.7 Concluding Remarks 255 -- Exercises 257 -- A BASIC PROBABILITY REVIEW 259 -- A.1 Sample Spaces and Events 259 -- A.2 Definition of Probability 260 -- A.3 Borel-Cantelli Lemmas 261 -- A.4 Conditional Probability 262 -- A.5 Random Variables 263 -- A.6 Discrete Random Variables 265 -- A.7 Expectation 266 -- A.8 Conditional Expectation 268 -- A.9 Variance 269 -- A.10 Vector Random Variables 270 -- A.11 The Multivariate Gaussian 271 -- A.12 Convergence of Random Sequences 273 -- A.13 Limiting Theorems 275 -- B VAPNIK-CHERVONENKIS THEORY 277 -- B.1 Shatter Coefficients 277 -- B.2 The VC Dimension 278 -- B.3 VC Theory of Classification 279 -- B.3.1 Linear Classification Rules 279 -- B.3.2 kNN Classification Rule 280 -- B.3.3 Classification Trees 280 -- B.3.4 Nonlinear SVMs 281 -- B.3.5 Neural Networks 281 -- B.3.6 Histogram Rules 281 -- B.4 Vapnik-Chervonenkis Theorem 282 -- C DOUBLE ASYMPTOTICS 285 -- BIBLIOGRAPHY 291 -- AUTHOR INDEX 301 -- SUBJECT INDEX 305. |
| Record Nr. | UNINA-9910830222903321 |
|
Braga-Neto Ulisses de Mendon AÀca
|
||
| Chichester, West Sussex : , : Wiley Blackwell, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Error theory as applied to mapping, charting, and geodesy [[electronic resource]]
| Error theory as applied to mapping, charting, and geodesy [[electronic resource]] |
| Pubbl/distr/stampa | Fairfax, Va. : , : Defense Mapping Agency, , [1991] |
| Descrizione fisica | 1 volume (various pagings) : digital, PDF file |
| Collana | DMA technical report |
| Soggetto topico |
Cartography
Error analysis (Mathematics) |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910696616103321 |
| Fairfax, Va. : , : Defense Mapping Agency, , [1991] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Estimating the error of numerical solutions of systems of reaction-diffusion equations / / Donald J. Estep, Mats G. Larson, Roy D. Williams
| Estimating the error of numerical solutions of systems of reaction-diffusion equations / / Donald J. Estep, Mats G. Larson, Roy D. Williams |
| Autore | Estep Donald J. <1959-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2000] |
| Descrizione fisica | 1 online resource (125 p.) |
| Disciplina |
510 s
515/.353 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Reaction-diffusion equations
Numerical calculations Error analysis (Mathematics) |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0287-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""1.1. Numerical analysis and reaction-diffusion equations""; ""1.2. The limitations of classic a priori error analysis""; ""1.3. What we do and don't do in this paper""; ""1.4. A brief overview of related work""; ""1.5. The plan of the paper""; ""Acknowledgments""; ""Chapter 2. A framework for a posteriori error estimation""; ""2.1. The continuous problem and its discretization""; ""2.2. The residual error""; ""2.3. The dual problem and a formula for the error""; ""2.4. The stability factors and the a posteriori error estimate""
""Chapter 3. The size of the residual errors and stability factors""""3.1. The size of the residual errors""; ""3.2. The size of the stability factors""; ""3.3. Application of the analysis to systems with constant diffusion""; ""3.4. The a posteriori estimate and convergence""; ""Chapter 4. Computational error estimation""; ""4.1. Two examples and a stability factor gallery""; ""4.2. Choosing data for the dual problem""; ""4.3. Linearization and the approximate dual problem""; ""4.4. A test of the accuracy and reliability of the error estimate""; ""4.5. Some details of implementation"" ""4.6. Numerical results for the nine models""""Chapter 5. Preservation of invariant rectangles under discretization""; ""5.1. Invariant rectangles and convergence""; ""5.2. Preservation of a ""fuzzy"" invariant rectangle""; ""5.3. Exact preservation of an invariant rectangle""; ""Chapter 6. Details of the analysis in Chapter 2""; ""Chapter 7. Details of the analysis in Chapter 3""; ""Chapter 8. Details of the analysis in Chapter 5""; ""Bibliography"" |
| Record Nr. | UNINA-9910480413403321 |
|
Estep Donald J. <1959->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2000] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Estimating the error of numerical solutions of systems of reaction-diffusion equations / / Donald J. Estep, Mats G. Larson, Roy D. Williams
| Estimating the error of numerical solutions of systems of reaction-diffusion equations / / Donald J. Estep, Mats G. Larson, Roy D. Williams |
| Autore | Estep Donald J. <1959-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2000] |
| Descrizione fisica | 1 online resource (125 p.) |
| Disciplina |
510 s
515/.353 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Reaction-diffusion equations
Numerical calculations Error analysis (Mathematics) |
| ISBN | 1-4704-0287-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""1.1. Numerical analysis and reaction-diffusion equations""; ""1.2. The limitations of classic a priori error analysis""; ""1.3. What we do and don't do in this paper""; ""1.4. A brief overview of related work""; ""1.5. The plan of the paper""; ""Acknowledgments""; ""Chapter 2. A framework for a posteriori error estimation""; ""2.1. The continuous problem and its discretization""; ""2.2. The residual error""; ""2.3. The dual problem and a formula for the error""; ""2.4. The stability factors and the a posteriori error estimate""
""Chapter 3. The size of the residual errors and stability factors""""3.1. The size of the residual errors""; ""3.2. The size of the stability factors""; ""3.3. Application of the analysis to systems with constant diffusion""; ""3.4. The a posteriori estimate and convergence""; ""Chapter 4. Computational error estimation""; ""4.1. Two examples and a stability factor gallery""; ""4.2. Choosing data for the dual problem""; ""4.3. Linearization and the approximate dual problem""; ""4.4. A test of the accuracy and reliability of the error estimate""; ""4.5. Some details of implementation"" ""4.6. Numerical results for the nine models""""Chapter 5. Preservation of invariant rectangles under discretization""; ""5.1. Invariant rectangles and convergence""; ""5.2. Preservation of a ""fuzzy"" invariant rectangle""; ""5.3. Exact preservation of an invariant rectangle""; ""Chapter 6. Details of the analysis in Chapter 2""; ""Chapter 7. Details of the analysis in Chapter 3""; ""Chapter 8. Details of the analysis in Chapter 5""; ""Bibliography"" |
| Record Nr. | UNINA-9910788841503321 |
|
Estep Donald J. <1959->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2000] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Estimating the error of numerical solutions of systems of reaction-diffusion equations / / Donald J. Estep, Mats G. Larson, Roy D. Williams
| Estimating the error of numerical solutions of systems of reaction-diffusion equations / / Donald J. Estep, Mats G. Larson, Roy D. Williams |
| Autore | Estep Donald J. <1959-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2000] |
| Descrizione fisica | 1 online resource (125 p.) |
| Disciplina |
510 s
515/.353 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Reaction-diffusion equations
Numerical calculations Error analysis (Mathematics) |
| ISBN | 1-4704-0287-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""1.1. Numerical analysis and reaction-diffusion equations""; ""1.2. The limitations of classic a priori error analysis""; ""1.3. What we do and don't do in this paper""; ""1.4. A brief overview of related work""; ""1.5. The plan of the paper""; ""Acknowledgments""; ""Chapter 2. A framework for a posteriori error estimation""; ""2.1. The continuous problem and its discretization""; ""2.2. The residual error""; ""2.3. The dual problem and a formula for the error""; ""2.4. The stability factors and the a posteriori error estimate""
""Chapter 3. The size of the residual errors and stability factors""""3.1. The size of the residual errors""; ""3.2. The size of the stability factors""; ""3.3. Application of the analysis to systems with constant diffusion""; ""3.4. The a posteriori estimate and convergence""; ""Chapter 4. Computational error estimation""; ""4.1. Two examples and a stability factor gallery""; ""4.2. Choosing data for the dual problem""; ""4.3. Linearization and the approximate dual problem""; ""4.4. A test of the accuracy and reliability of the error estimate""; ""4.5. Some details of implementation"" ""4.6. Numerical results for the nine models""""Chapter 5. Preservation of invariant rectangles under discretization""; ""5.1. Invariant rectangles and convergence""; ""5.2. Preservation of a ""fuzzy"" invariant rectangle""; ""5.3. Exact preservation of an invariant rectangle""; ""Chapter 6. Details of the analysis in Chapter 2""; ""Chapter 7. Details of the analysis in Chapter 3""; ""Chapter 8. Details of the analysis in Chapter 5""; ""Bibliography"" |
| Record Nr. | UNINA-9910812748103321 |
|
Estep Donald J. <1959->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2000] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Finite element analysis with error estimators [[electronic resource] ] : an introduction to the FEM and adaptive error analysis for engineering students / / J.E. Akin
| Finite element analysis with error estimators [[electronic resource] ] : an introduction to the FEM and adaptive error analysis for engineering students / / J.E. Akin |
| Autore | Akin J. E |
| Pubbl/distr/stampa | Oxford, : Elsevier, 2005 |
| Descrizione fisica | 1 online resource (465 p.) |
| Disciplina | 620.00151825 |
| Soggetto topico |
Finite element method
Structural analysis (Engineering) Error analysis (Mathematics) |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-01611-X
9786611016111 0-08-047275-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Front matter; Half Title Page; Title Page; Copyright; Contents; Preface; Features of the text and accompanying resources; Notation; 1. Introduction; 1.1 Finite element methods; 1.2 Capabilities of FEA; 1.3 Outline of finite element procedures; 1.4 Assembly into the system equations; 1.5 Error concepts; 1.6 Exercises; 1.7 Bibliography; 2. Mathematical preliminaries; 2.1 Introduction; 2.2 Linear spaces and norms; 2.3 Sobolev norms; 2.4 Dual problem, self-adjointness; 2.5 Weighted residuals; 2.6 Boundary condition terms; 2.7 Adding more unknowns; 2.8 Numerical integration
2.9 Integration by parts 2.10 Finite element model problem; 2.11 Continuous nodal flux recovery; 2.12 A one-dimensional example error analysis; 2.13 General boundary condition choices; 2.14 General matrix partitions; 2.15 Elliptic boundary value problems; 2.16 Initial value problems; 2.17 Eigen-problems; 2.18 Equivalent forms; 2.19 Exercises; 2.20 Bibliography; 3. Element interpolation and local coordinates; 3.1 Introduction; 3.2 Linear interpolation; 3.3 Quadratic interpolation; 3.4 Lagrange interpolation; 3.5 Hermitian interpolation; 3.6 Hierarchical interpolation 3.7 Space-time interpolations 3.8 Nodally exact interpolations; 3.9 Interpolation error; 3.10 Gradient estimates; 3.11 Exercises; 3.12 Bibliography; 4. One-dimensional integration; 4.1 Introduction; 4.2 Local coordinate Jacobian; 4.3 Exact polynomial integration; 4.4 Numerical integration; 4.5 Variable Jacobians; 4.6 Exercises; 4.7 Bibliography; 5. Error estimates for elliptic problems; 5.1 Introduction; 5.2 Error estimates; 5.3 Hierarchical error indicator; 5.4 Flux balancing error estimates; 5.5 Element adaptivity; 5.6 H-adaptivity; 5.7 P-adaptivity; 5.8 HP-adaptivity; 5.9 Exercises 5.10 Bibliography 6. Super-convergent patch recovery; 6.1 Patch implementation database; 6.2 SCP nodal flux averaging; 6.3 Computing the SCP element error estimates; 6.4 Hessian matrix; 6.5 Exercises; 6.6 Bibliography; 7. Variational methods; 7.1 Introduction; 7.2 Structural mechanics; 7.3 Finite element analysis; 7.4 Continuous elastic bar; 7.5 Thermal loads on a bar; 7.6 Reaction flux recovery for an element; 7.7 Heat transfer in a rod; 7.8 Element validation; 7.9 Euler's equations of variational calculus; 7.10 Exercises; 7.11 Bibliography; 8. Cylindrical analysis problems; 8.1 Introduction 8.2 Heat conduction in a cylinder 8.3 Cylindrical stress analysis; 8.4 Exercises; 8.5 Bibliography; 9. General interpolation; 9.1 Introduction; 9.2 Unit coordinate interpolation; 9.3 Natural coordinates; 9.4 Isoparametric and subparametric elements; 9.5 Hierarchical interpolation; 9.6 Differential geometry; 9.7 Mass properties; 9.8 Interpolation error; 9.9 Element distortion; 9.10 Space-time interpolation; 9.11 Exercises; 9.12 Bibliography; 10. Integration methods; 10.1 Introduction; 10.2 Unit coordinate integration; 10.3 Simplex coordinate integration; 10.4 Numerical integration 10.5 Typical source distribution integrals |
| Record Nr. | UNINA-9910457719003321 |
|
Akin J. E
|
||
| Oxford, : Elsevier, 2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Finite element analysis with error estimators [[electronic resource] ] : an introduction to the FEM and adaptive error analysis for engineering students / / J.E. Akin
| Finite element analysis with error estimators [[electronic resource] ] : an introduction to the FEM and adaptive error analysis for engineering students / / J.E. Akin |
| Autore | Akin J. E |
| Pubbl/distr/stampa | Oxford, : Elsevier, 2005 |
| Descrizione fisica | 1 online resource (465 p.) |
| Disciplina | 620.00151825 |
| Soggetto topico |
Finite element method
Structural analysis (Engineering) Error analysis (Mathematics) |
| ISBN |
1-281-01611-X
9786611016111 0-08-047275-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Front matter; Half Title Page; Title Page; Copyright; Contents; Preface; Features of the text and accompanying resources; Notation; 1. Introduction; 1.1 Finite element methods; 1.2 Capabilities of FEA; 1.3 Outline of finite element procedures; 1.4 Assembly into the system equations; 1.5 Error concepts; 1.6 Exercises; 1.7 Bibliography; 2. Mathematical preliminaries; 2.1 Introduction; 2.2 Linear spaces and norms; 2.3 Sobolev norms; 2.4 Dual problem, self-adjointness; 2.5 Weighted residuals; 2.6 Boundary condition terms; 2.7 Adding more unknowns; 2.8 Numerical integration
2.9 Integration by parts 2.10 Finite element model problem; 2.11 Continuous nodal flux recovery; 2.12 A one-dimensional example error analysis; 2.13 General boundary condition choices; 2.14 General matrix partitions; 2.15 Elliptic boundary value problems; 2.16 Initial value problems; 2.17 Eigen-problems; 2.18 Equivalent forms; 2.19 Exercises; 2.20 Bibliography; 3. Element interpolation and local coordinates; 3.1 Introduction; 3.2 Linear interpolation; 3.3 Quadratic interpolation; 3.4 Lagrange interpolation; 3.5 Hermitian interpolation; 3.6 Hierarchical interpolation 3.7 Space-time interpolations 3.8 Nodally exact interpolations; 3.9 Interpolation error; 3.10 Gradient estimates; 3.11 Exercises; 3.12 Bibliography; 4. One-dimensional integration; 4.1 Introduction; 4.2 Local coordinate Jacobian; 4.3 Exact polynomial integration; 4.4 Numerical integration; 4.5 Variable Jacobians; 4.6 Exercises; 4.7 Bibliography; 5. Error estimates for elliptic problems; 5.1 Introduction; 5.2 Error estimates; 5.3 Hierarchical error indicator; 5.4 Flux balancing error estimates; 5.5 Element adaptivity; 5.6 H-adaptivity; 5.7 P-adaptivity; 5.8 HP-adaptivity; 5.9 Exercises 5.10 Bibliography 6. Super-convergent patch recovery; 6.1 Patch implementation database; 6.2 SCP nodal flux averaging; 6.3 Computing the SCP element error estimates; 6.4 Hessian matrix; 6.5 Exercises; 6.6 Bibliography; 7. Variational methods; 7.1 Introduction; 7.2 Structural mechanics; 7.3 Finite element analysis; 7.4 Continuous elastic bar; 7.5 Thermal loads on a bar; 7.6 Reaction flux recovery for an element; 7.7 Heat transfer in a rod; 7.8 Element validation; 7.9 Euler's equations of variational calculus; 7.10 Exercises; 7.11 Bibliography; 8. Cylindrical analysis problems; 8.1 Introduction 8.2 Heat conduction in a cylinder 8.3 Cylindrical stress analysis; 8.4 Exercises; 8.5 Bibliography; 9. General interpolation; 9.1 Introduction; 9.2 Unit coordinate interpolation; 9.3 Natural coordinates; 9.4 Isoparametric and subparametric elements; 9.5 Hierarchical interpolation; 9.6 Differential geometry; 9.7 Mass properties; 9.8 Interpolation error; 9.9 Element distortion; 9.10 Space-time interpolation; 9.11 Exercises; 9.12 Bibliography; 10. Integration methods; 10.1 Introduction; 10.2 Unit coordinate integration; 10.3 Simplex coordinate integration; 10.4 Numerical integration 10.5 Typical source distribution integrals |
| Record Nr. | UNINA-9910784454003321 |
|
Akin J. E
|
||
| Oxford, : Elsevier, 2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Finite element analysis with error estimators [[electronic resource] ] : an introduction to the FEM and adaptive error analysis for engineering students / / J.E. Akin
| Finite element analysis with error estimators [[electronic resource] ] : an introduction to the FEM and adaptive error analysis for engineering students / / J.E. Akin |
| Autore | Akin J. E |
| Pubbl/distr/stampa | Oxford, : Elsevier, 2005 |
| Descrizione fisica | 1 online resource (465 p.) |
| Disciplina | 620.00151825 |
| Soggetto topico |
Finite element method
Structural analysis (Engineering) Error analysis (Mathematics) |
| ISBN |
1-281-01611-X
9786611016111 0-08-047275-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Front matter; Half Title Page; Title Page; Copyright; Contents; Preface; Features of the text and accompanying resources; Notation; 1. Introduction; 1.1 Finite element methods; 1.2 Capabilities of FEA; 1.3 Outline of finite element procedures; 1.4 Assembly into the system equations; 1.5 Error concepts; 1.6 Exercises; 1.7 Bibliography; 2. Mathematical preliminaries; 2.1 Introduction; 2.2 Linear spaces and norms; 2.3 Sobolev norms; 2.4 Dual problem, self-adjointness; 2.5 Weighted residuals; 2.6 Boundary condition terms; 2.7 Adding more unknowns; 2.8 Numerical integration
2.9 Integration by parts 2.10 Finite element model problem; 2.11 Continuous nodal flux recovery; 2.12 A one-dimensional example error analysis; 2.13 General boundary condition choices; 2.14 General matrix partitions; 2.15 Elliptic boundary value problems; 2.16 Initial value problems; 2.17 Eigen-problems; 2.18 Equivalent forms; 2.19 Exercises; 2.20 Bibliography; 3. Element interpolation and local coordinates; 3.1 Introduction; 3.2 Linear interpolation; 3.3 Quadratic interpolation; 3.4 Lagrange interpolation; 3.5 Hermitian interpolation; 3.6 Hierarchical interpolation 3.7 Space-time interpolations 3.8 Nodally exact interpolations; 3.9 Interpolation error; 3.10 Gradient estimates; 3.11 Exercises; 3.12 Bibliography; 4. One-dimensional integration; 4.1 Introduction; 4.2 Local coordinate Jacobian; 4.3 Exact polynomial integration; 4.4 Numerical integration; 4.5 Variable Jacobians; 4.6 Exercises; 4.7 Bibliography; 5. Error estimates for elliptic problems; 5.1 Introduction; 5.2 Error estimates; 5.3 Hierarchical error indicator; 5.4 Flux balancing error estimates; 5.5 Element adaptivity; 5.6 H-adaptivity; 5.7 P-adaptivity; 5.8 HP-adaptivity; 5.9 Exercises 5.10 Bibliography 6. Super-convergent patch recovery; 6.1 Patch implementation database; 6.2 SCP nodal flux averaging; 6.3 Computing the SCP element error estimates; 6.4 Hessian matrix; 6.5 Exercises; 6.6 Bibliography; 7. Variational methods; 7.1 Introduction; 7.2 Structural mechanics; 7.3 Finite element analysis; 7.4 Continuous elastic bar; 7.5 Thermal loads on a bar; 7.6 Reaction flux recovery for an element; 7.7 Heat transfer in a rod; 7.8 Element validation; 7.9 Euler's equations of variational calculus; 7.10 Exercises; 7.11 Bibliography; 8. Cylindrical analysis problems; 8.1 Introduction 8.2 Heat conduction in a cylinder 8.3 Cylindrical stress analysis; 8.4 Exercises; 8.5 Bibliography; 9. General interpolation; 9.1 Introduction; 9.2 Unit coordinate interpolation; 9.3 Natural coordinates; 9.4 Isoparametric and subparametric elements; 9.5 Hierarchical interpolation; 9.6 Differential geometry; 9.7 Mass properties; 9.8 Interpolation error; 9.9 Element distortion; 9.10 Space-time interpolation; 9.11 Exercises; 9.12 Bibliography; 10. Integration methods; 10.1 Introduction; 10.2 Unit coordinate integration; 10.3 Simplex coordinate integration; 10.4 Numerical integration 10.5 Typical source distribution integrals |
| Record Nr. | UNINA-9910825031703321 |
|
Akin J. E
|
||
| Oxford, : Elsevier, 2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Finite element analysis with error estimators [e-book] : an introduction to the FEM and adaptive error analysis for engineering students / J.E. Akin
| Finite element analysis with error estimators [e-book] : an introduction to the FEM and adaptive error analysis for engineering students / J.E. Akin |
| Autore | Akin, J. E. |
| Pubbl/distr/stampa | Amsterdam ; Boston : Elsevier/Butterworth-Heinemann, 2005 |
| Descrizione fisica | xviii, 447 p. : ill. ; 25 cm |
| Disciplina | 620.00151825 |
| Soggetto topico |
Finite element method
Structural analysis (Engineering) Error analysis (Mathematics) |
| Soggetto genere / forma | Electronic books. |
| ISBN |
9780750667227
0750667222 |
| Formato | Risorse elettroniche  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Introduction, Mathematical Premliminaries, Element Interpolation and Local Coordinates, One-Dimensional Integration, Error Estimation for Elliptic Problems, Super-convergent Patch Recovery, Variational Methods, Cylindrical Analysis Problems, General Interpolation, Integration Methods, Scalar Fields, Vector Fields, Index, Solutions Manual |
| Record Nr. | UNISALENTO-991003229189707536 |
|
Akin, J. E.
|
||
| Amsterdam ; Boston : Elsevier/Butterworth-Heinemann, 2005 | ||
| Risorse elettroniche | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
