Mathematical principles for scientific computing and visualization:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Wellesley, Mass.
Peters
2008
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 280 S. Ill., graph. Darst. |
| ISBN: | 9781568813219 |
Staff View
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Record in the Search Index
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| adam_text | Titel: Mathematical principles for scientific computing and visualization
Autor: Farin, Gerald E.
Jahr: 2008
Contents
Preface xi
1 Introduction 1
2 Computational Basics 5
2.1 Algorithms...................... 5
2.2 Floating-Point Numbers .............. 6
2.3 Errors......................... 7
2.4 Case Study: The 1991 Scud Attack........ 10
2.5 Problems and Experiments............. 11
3 Coordinate Systems 13
3.1 Cartesian Coordinate Systems........... 13
3.2 Polar, Spherical, and Cylindrical
Coordinate Systems................. 16
3.3 Case Study: UTM Coordinates .......... 19
3.4 Local and Global Coordinates........... 21
3.5 Homogeneous Coordinates............. 25
3.6 Problems and Experiments............. 26
4 Background: Numerical Linear Algebra 27
4.1 Linear Spaces and Vectors............. 27
4.2 Linear Independence and Subspaces........ 29
4.3 Linear Maps and Matrices............. 31
4.4 Lengths and Volumes................ 37
4.5 Summary of Matrix Rules ............. 40
4.6 Problems and Experiments............. 40
5 Solving Linear Systems 41
5.1 Case Study: Mixing Chemicals........... 41
5.2 Linear System Basics................ 42
5.3 Gauss Elimination.................. 43
5.4 Stability....................... 45
5.5 Vector Norms and Sequences............ 46
5.6 Iterative System Solvers .............. 48
5.7 Case Study: Fluid Flow............... 51
5.8 Overdetermined Systems.............. 53
5.9 Case Study: Femoral Head Reconstruction .... 54
5.10 Problems and Experiments............. 55
6 Eigen-Problems 57
6.1 Eigenvalues...................... 58
6.2 The Power Method................. 60
6.3 Case Study: PageRank............... 61
6.4 Jacobi Iteration................... 63
6.5 Eigenvalues and Determinants........... 66
6.6 Singular Value Decomposition........... 67
6.7 The Condition Number............... 70
6.8 The Pseudoinverse.................. 70
6.9 The Principal Components Analysis........ 72
6.10 Case Study: Eigenfaces............... 73
6.11 Singular Values, Volumes, and Determinants ... 75
6.12 Problems and Experiments............. 76
7 Background: Numerical Calculus 77
7.1 Functions....................... 77
7.2 Limits ........................ 80
7.3 Integrals....................... 81
7.4 Derivatives...................... 83
7.5 Function Spaces................... 86
7.6 Problems and Experiments ............. 88
8 Data Fitting 91
8.1 Taylor Approximation................ 91
8.2 Piecewise Linear Interpolation........... 92
8.3 Polynomial Interpolation.............. 92
8.4 Polynomial Least Squares Approximation..... 94
8.5 General Least Squares Approximation....... 98
8.6 B-Spline Interpolation................ 99
8.7 B-Spline Least Squares Approximation...... 104
8.8 Integrals and Derivatives.............. 105
8.9 Problems and Experiments............. 107
9 Computing Dynamic Processes 109
9.1 Background ..................... 109
9.2 Euler s Method................... Ill
9.3 Heun s Method ................... 113
9.4 Boundary Values .................. 115
9.5 ODEs and Dynamical Systems........... 117
9.6 Case Study: The Lorenz Attractor......... 120
9.7 Problems and Experiments............. 122
10 Finding Roots 123
10.1 The Piecewise Linear Approach.......... 123
10.2 The Newton-Raphson Method........... 125
10.3 Case Study: Computing the Square Root..... 127
10.4 Bisection....................... 128
10.5 Case Study: Wilkinson Polynomials........ 129
10.6 Problems and Experiments............. 129
11 Computing with Multivariate Functions 131
11.1 Bivariate Functions................. 131
11.2 Bilinear Interpolation................ 135
11.3 Quadratic Forms................... 137
11.4 Contouring...................... 138
11.5 The Newton-Raphson Method........... 140
11.6 Partial Differential Equations ........... 142
11.7 Trivariate Functions................. 145
11.8 Problems and Experiments............. 147
12 Visualizing Empirical Data 149
12.1 Scatter Plots, Correlations, and Regression . . . 149
12.2 PCA Revisited.................... 153
12.3 Histograms, Bar Charts, and Pie Charts..... 155
12.4 Box Plots....................... 159
12.5 Log Plots....................... 161
12.6 Problems and Experiments............. 163
13 Facets 165
13.1 Triangles....................... 165
13.2 Barycentric Coordinates.............. 167
13.3 Planes ........................ 169
13.4 Polygons and Polyhedra .............. 172
13.5 Triangle Meshes................ . . . 174
13.6 Case Study: 3D Archiving............ . 178
13.7 Analyzing Triangle Meshes............. 179
13.8 Delaunay Meshes and Voronoi Diagrams..... 181
13.9 Case Study: Bark Beetles.............. 184
13.10 Other Meshes.................... 184
13.11 Problems and Experiments............. 186
14 Visualizing Scalar Values over 2D Data 189
14.1 Height Maps..................... 192
14.2 Color Maps...................... 194
14.3 Contours....................... 197
14.4 Case Study: GIS................... 204
14.5 Image Segmentation................. 206
14.6 Problems and Experiments............. 208
15 Volume Visualization 209
15.1 Scalar Data over a Volume............. 209
15.2 Contouring...................... 215
15.3 Case Study: Health Care.............. 218
15.4 Direct Volume Rendering.............. 219
15.5 Transfer Functions.................. 222
15.6 Comparison of Contouring and DVR....... 224
15.7 Case Study: Visible Human Project........ 225
15.8 Data Cutting.................... 226
15.9 Vector Fields..................... 227
15.10 Tensor Fields..................... 229
15.11 Haptic Visualization................. 230
15.12 Problems and Experiments............. 231
16 Background: Computer Graphics 233
16.1 Color Models..................... 234
16.2 The Graphics Pipeline ............... 236
16.3 Illumination Models................. 252
16.4 Texture Mapping.................. 261
16.5 Sampling, Smoothing, Reduction ......... 263
16.6 Problems and Experiments............. 266
Bibliography 269
Index 271
|
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| dewey-tens | 500 - Natural sciences and mathematics |
| discipline | Allgemeine Naturwissenschaft Informatik |
| format | Book |
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| isbn | 9781568813219 |
| language | English |
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| physical | XIV, 280 S. Ill., graph. Darst. |
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| spelling | Farin, Gerald E. 1953- Verfasser (DE-588)109438760 aut Mathematical principles for scientific computing and visualization Gerald Farin ; Dianne Hansford Wellesley, Mass. Peters 2008 XIV, 280 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Computervisualistik (DE-588)7535806-2 gnd rswk-swf Interpolation (DE-588)4162121-9 gnd rswk-swf Voronoi-Diagramm (DE-588)4226013-9 gnd rswk-swf Computervisualistik (DE-588)7535806-2 s Interpolation (DE-588)4162121-9 s Voronoi-Diagramm (DE-588)4226013-9 s DE-604 Hansford, Dianne Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020173975&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Farin, Gerald E. 1953- Hansford, Dianne Mathematical principles for scientific computing and visualization Computervisualistik (DE-588)7535806-2 gnd Interpolation (DE-588)4162121-9 gnd Voronoi-Diagramm (DE-588)4226013-9 gnd |
| subject_GND | (DE-588)7535806-2 (DE-588)4162121-9 (DE-588)4226013-9 |
| title | Mathematical principles for scientific computing and visualization |
| title_auth | Mathematical principles for scientific computing and visualization |
| title_exact_search | Mathematical principles for scientific computing and visualization |
| title_full | Mathematical principles for scientific computing and visualization Gerald Farin ; Dianne Hansford |
| title_fullStr | Mathematical principles for scientific computing and visualization Gerald Farin ; Dianne Hansford |
| title_full_unstemmed | Mathematical principles for scientific computing and visualization Gerald Farin ; Dianne Hansford |
| title_short | Mathematical principles for scientific computing and visualization |
| title_sort | mathematical principles for scientific computing and visualization |
| topic | Computervisualistik (DE-588)7535806-2 gnd Interpolation (DE-588)4162121-9 gnd Voronoi-Diagramm (DE-588)4226013-9 gnd |
| topic_facet | Computervisualistik Interpolation Voronoi-Diagramm |
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