ALBERT

Note: Auch als Internetausg.

Note: Erscheinungsjahr in Vorlageform:2009

Note: Table of Contents 1 Introduction 1.1 Scripting versus Traditional Programming 1.1.1 Why Scripting is Useful in Computational Science 1.1.2 Classification of Programming Languages 1.1.3 Productive Pairs of Programming Languages 1.1.4 Gluing Existing Applications 1.1.5 Scripting Yields Shorter Code 1.1.6 Efficiency 1.1.7 Type-Specification (Declaration) of Variables 1.1.8 Flexible Function Interfaces 1.1.9 Interactive Computing 1.1.10 Creating Code at Run Time 1.1.11 Nested Heterogeneous Data Structures 1.1.12 GUI Programming 1.1.13 Mixed Language Programming 1.1.14 When to Choose a Dynamically Typed Language 1.1.15 Why Python? 1.1.16 Script or Program? 1.2 Preparations for Working with This Book 2 Getting Started with Python Scripting 2.1 A Scientific Hello World Script 2.1.1 Executing Python Scripts 2.1.2 Dissection of the Scientific Hello World Script 2.2 Working with Files and Data 2.2.1 Problem Specification 2.2.2 The Complete Code 2.2.3 Dissection 2.2.4 Working with Files in Memory 2.2.5 Array Computing 2.2.6 Interactive Computing and Debugging 2. 2.7 Efficiency Measurements 2.2.8 Exercises 2.3 Gluing Stand-Alone Applications 2.3.1 The Simulation Code 2.3.2 Using Gnuplot to Visualize Curves 2.3.3 Functionality of the Script 2.3.4 The Complete Code 2.3.5 Dissection 2.3.6 Exercises 2.4 Conducting Numerical Experiments 2.4.1 Wrapping a Loop Around Another Script 2.4.2 Generating an HTML Report 2.4.3 Making Animations 2.4.4 Varying Any Parameter 2.5 File Format Conversion 2.5.1 A Simple Read/Write Script 2.5.2 Storing Data in Dictionaries and Lists 2.5.3 Making a Module with Functions 2.5.4 Exercises 3 Basic Python 3.1 Introductory Topics 3.1.1 Recommended Python Documentation 3.1.2 Control Statements 3.1.3 Running Applications 3.1.4 File Reading and Writing 3.1.5 Output Formatting 3.2 Variables of Different Types 3.2.1 Boolean Types 3.2.2 The None Variable 3.2.3 Numbers and Numerical Expressions 3.2.4 Lists and Tuples 3.2.5 Dictionaries 3.2.6 Splitting and Joining Text 3.2.7 String Operations 3.2.8 Text Processing 3.2.9 The Basics of a Python Class 3.2.10 Copy and Assignment 3.2.11 Determining a Variable's Type 3.2.12 Exercises 3.3 Functions 3.3.1 Keyword Arguments 3.3.2 Doc Strings 3.3.3 Variable Number of Arguments 3.3.4 Call by Reference 3.3.5 Treatment of Input and Output Arguments 3.3.6 Function Objects 3.4 Working with Files and Directories 3.4.1 Listing Files in a Directory 3.4.2 Testing File Types 3.4.3 Removing Files and Directories 3.4.4 Copying and Renaming Files 3.4.5 Splitting Pathnames 3.4.6 Creating and Moving to Directories 3.4.7 Traversing Directory Trees 3.4.8 Exercises 4 Numerical Computing in Python 4.1 A Quick NumPy Primer 4.1.1 Creating Arrays 4.1.2 Array Indexing 4.1.3 Loops over Arrays 4.1.4 Array Computations 4.1.5 More Array Functionality 4.1.6 Type Testing 4.1.7 Matrix Objects 4.1.8 Exercises 4.2 Vectorized Algorithms 4.2.1 From Scalar to Array in Function Arguments 4.2.2 Slicing 4.2.3 Exercises 4.3 More Advanced Array Computing 4.3.1 Random Numbers 4.3.2 Linear Algebra 4.3.3 Plotting 4.3.4 Example: Curve Fitting 4.3.5 Arrays on Structured Grids 4.3.6 File I/O with NumPy Arrays 4.3.7 Functionality in the Numpyutils Module 4.3.8 Exercises 4.4 Other Tools for Numerical Computations 4.4.1 The ScientificPython Package 4.4.2 The SciPy Package 4.4.3 The Python- Matlab Interface 3 4.4.4 Symbolic Computing in Python 4.4.5 Some Useful Python Modules 5 Combining Python with Fortran, C, and C++ 5.1 About Mixed Language Programming 5.1.1 Applications of Mixed Language Programming 5.1.2 Calling C from Python 5.1.3 Automatic Generation of Wrapper Code 5.2 Scientific Hello World Examples 5.2.1 Combining Python and Fortran 5.2.2 Combining Python and C 5.2.3 Combining Python and C++ Functions 5.2.4 Combining Python and C++ Classes 5.2.5 Exercises 5.3 A Simple Computational Steering Example 5.3.1 Modified Time Loop for Repeated Simulations 5.3.2 Creating a P ython Interface 5.3.3 The Steering Python Script 5.3.4 Equipping the Steering Script with a GUI 5.4 Scripting Interfaces to Large Libraries 6 Introduction to GUI Programming 6.1 Scientific Hello World GUI 6.1.1 Introductory Topics 6.1.2 The First Python/Tkinter Encounter 6.1.3 Binding Events 6.1.4 Changing the Layout 6.1.5 The Final Scientific Hello World GUI 6.1.6 An Alternative to Tkinter Variables 6.1.7 About the Pack Command 6.1.8 An Introduction to the Grid Geometry Manager 6.1.9 Implementing a GUI as a Class 6.1.10 A Simple Graphical Function Evaluator 6.1.11 Exercises 6.2 Adding GUis to Scripts 6.2.1 A Simulation and Visualization Script with a GUI 6.2.2 Improving the Layout 6.2.3 Exercises 6.3 A List of Common Widget Operations 6.3.1 Frame 6.3.2 Label 6.3.3 Button 6.3.4 Text Entry 6.3.5 Balloon Help 6.3.6 Option Menu 6.3.7 Slider 6.3.8 Check Button 6.3.9 Making a Simple Megawidget 6.3.10 Menu Bar 6.3.11 List Data 6.3.12 Listbox 6.3.13 Radio Button 6.3.14 Combo Box 6.3.15 Message Box 6.3.16 User-Defined Dialogs 6.3.17 Color-Picker Dialogs 6.3.18 File Selection Dialogs 6.3.19 Toplevel 6.3.20 Some Other Types of Widgets 6.3.21 Adapting Widgets to the User's Resize Actions 6.3.22 Customizing Fonts and Colors 6.3.23 Widget Overview 6.3.24 Exercises 7 Web Interfaces and CGI Programming 7.1 Introductory CGI Scripts 7.1.1 Web Forms and CGI Scripts 7.1.2 Generating Forms in CGI Scripts 7.1.3 Debugging CGI Scripts 7.1.4 A General Shell Script Wrapper for CGI Scripts 7.1.5 Security Issues 7.2 Adding Web Interfaces to Scripts 7.2.1 A Class for Form Parameters 7.2.2 Calling Other Programs 7.2.3 Running Simulations 7.2.4 Getting a CGI Script to Work 7.2.5 Using Web Applications from Scripts 7.2.6 Exercises 8 Advanced Python 8.1 Miscellaneous Topics 8.1.1 Parsing Command-Line Arguments 8.1.2 Platform-Dependent Operations 8.1.3 Run-Time Generation of Code 8.1.4 Exercises 8.2 Regular Expressions and Text Processing 8.2.1 Motivation 8.2.2 Special Characters 8.2.3 Regular Expressions for Real Numbers 8.2.4 Using Groups to Extract Parts of a Text 8.2.5 Extracting Interval Limits 8.2.6 Extracting Multiple Matches 8.2.7 Splitting Text 8.2.8 Pattern-Matching Modifiers 8.2.9 Substitution and Backreferences 8.2.10 Example: Swapping Arguments in Function Calls 8.2.11 A General Substitution Script 8.2.12 Debugging Regular Expressions 8.2.13 Exercises 8.3 Tools for Handling Data in Files 8.3.1 Writing and Reading Python Data Structures 8.3.2 Pickling Objects 8.3.3 Shelving Objects 8.3.4 Writing and Reading Zip and Tar Archive Files 8.3.5 Downloading Internet Files 8.3.6 Binary Input/Output 8.3.7 Exercises 8.4 A Database for NumPy Arrays 8.4.1 The Structure of the Database 8.4.2 Pickling 8.4.3 Formatted ASCII Storage 8.4.4 Shelving 8.4.5 Comparing the Various Techniques 8.5 Scripts Involving Local and Remote Hosts 8.5.1 Secure Shell Commands 8.5.2 Distributed Simulation and Visualization 8.5.3 Client/Server Programming 8.5.4 Threads 8.6 Classes 8.6.1 Class Programming 8.6.2 Checking the Class Type 8.6.3 Private Data 8.6.4 Static Data 8.6.5 Special Attributes 8.6.6 Special Methods 8.6.7 Multiple Inheritance 8.6.8 Using a Class as a C-like Structure 8.6.9 Attribute Access via String Names 8.6.10 New-Style Classes 8.6.11 Implementing Get/Set Functions via Properties 8.6.12 Subclassing Built-in Types 8.6.13 Building Class Interfaces at Run Time 8.6.14 Building Flexible Class Interfaces 8.6.15 Exercises 8.7 Scope of Variables 8.7.1 Global, Local, and Class Variables 8.7.2 Nested Functions 8.7.3 Dictionaries of Variables in Namespaces 8.8 Exceptions 8.8.1 Handling Exceptions 8.8.2 Raising Exceptions 8.9 Iterators 8.9.1 Constructing an Iterator 8.9.2 A Pointwise Grid Iterator 8.9.3 A Vectorized Grid Iterator 8.9.4 Generators 8.

Note: Erscheinungsjahr in Vorlageform:2008

Note: Erscheinungsjahr in Vorlageform:2008

Note: Zugl.: Innsbruck, Univ., Diss., 2004

Note: Erscheinungsjahr in Vorlageform:c 2007

Note: Inhalt: 1 Einleitung. - 1.1 Alltägliche Probleme. - 1.2 Uni- und multivariate Daten. - 1.3 Wege ins Statistiklabyrinth. - 2 Statistische Grundlagen. - 2.1 Einführung in die Terminologie. - 2.2 Datentypen -Skalenniveaus. - 2.3 Korrelation. - 2.4 Regression. - 2.5 Lineare Regression. - 2.6 Multiplelineare Regression. - 2.7 Unimodale Modelle - die Gauß'sche Regression. - 2.8 Logistische und Gauß'sche logistische Regression. - 2.9 Interaktionen. - 2.10 Gewichtetes Mittel. - 2.11 Partielle Analysen. - 3 Datenmanipulationen. - 3.1 Normalverteilung und Transformationen. - 3.2 Standardisierungen. - 3.3 Transponieren, Umkodieren und Maskieren. - 4 Ähnlichkeits- und Distanzmaße. - 4.1 Qualitative Ähnlichkeitsmaße. - 4.2 Quantitative Ähnlichkeitsmaße. - 4.3 Distanzmaße. - 4.4 Vergleich der geschilderten Koeffizienten. - 5 Ordinationen - das Prinzip. - 5.1 Dimensionsreduktion als Analysestrategie. - 5.2 Polare Ordination. - 6 Korrespondenzanalyse (CA). - 6.1 Das Prinzip. - 6.2 Mathematische Artefakte - Probleme der CA. - 6.3 DCA {Detrended Correspondence Analysis). - 6.4 Zusammenfassendes zu Problemen der CA und DCA. - 7 Interpretation von CA und DCA. - 7.1 Zur Skalierung und Interpretation der Ordinationsdiagramme. - 7.2 Umweltvariablen-Interaktionen von Effekten. - 7.3 Ordination und Umweltdaten. - 8 Kanonische Ordination (constrained ordination). - 8.1 Prinzip der Kanonischen Korrespondenzanalyse (CCA). - 8.2 Interpretation eines CCA-Diagramms. - 8.3 Forward selection bei kanonischen Ordinationen. - 8.4 Überprüfung einer CCA. - 9 Hauptkomponentenanalyse (PCA). - 9.1 Das Prinzip - geometrische Herleitung. - 9.2 Das Prinzip - der mathematische Ansatz. - 9.3 Optionen bei einer PCA. - 9.4 Stärken und Schwächen der PCA. - 9.5 Faktorenanalyse. - 10 Lineare Methoden und Umweltdaten: PCA und RDA. - 10.1 Indirekte Ordination. - 10.2 Kanonische Ordination - Prinzip der Redundanzanalyse. - 10.3 Interpretation einer RDA. - 11 Partielle Ordination und variance partitioning. - 11.1 Kovariablen. - 11.2 Partielle PCA, CA, DCA. - 11.3 Partielle kanonische Ordination. - 11.4 Variance partitioning. - 12 Multidimensionale Skalierung. - 12.1 Der andere Weg zum Ziel. - 12.2 Metrische Multidimensionale Skalierung - Hauptkoordinatenanalyse. - 12.3 Nichtmetrische Multidimensionale Skalierung. - 12.3.1 Das Prinzip. - 12.3.2 NMDS - Optionen und Probleme. - 12.3.3 Ablauf einer NMDS. - 13 Klassifikation - das Prinzip. - 13.1 Das Wesen von Klassifikationen. - 13.2 Die wichtigsten Klassifikationsstrategien. - 14 Agglomerative Klassifikationsverfahren. - 14.1Clusteranalyse - Grundlagen. - 14.2 Auswertung von Dendrogrammen. - 15 Divisive Klassifikationsverfahren. - 15.1 Ordination Space Partitioning. - 15.2 TWINSPAN. - 15.3 Ablauf einer TWINSPAN-Analyse. - 15.4 Kritik an der TWINSPAN-Analyse. - 16 Sonstige Verfahren zur Beschreibung von Gruppenstrukturen. - 16.1 Nichthierarchische agglomerative Verfahren. - 16.2 Nichthierarchische divisive Verfahren. - 16.3 Numerische "treue"-basierte Verfahren. - 16.4 Diskriminanzanalyse. - 16.4.1 Das Prinzip. - 16.4.2 Voraussetzungen. - 16.4.3 Gütekriterien/Prüfung der Ergebnisse. - 17 Permutationsbasierte Tests. - 17.1 Das Prinzip von Permutationstests. - 17.2 Test auf Signifikanz von Ordinationsachsen. - 17.3 Mantel-Test. - 17.4 Gruppenvergleiche - Mantel-Tests und MRPP. - 17.5 Procrustes-Analysen. - 17.6 Indicator Species Analysis. - 17.7 Ausblick Randomisierungsverfahren. - Literatur. - Sachverzeichnis.

Note: Contents Preface 1 Data Analysis in Earth Sciences 1.1 Introduction 1.2 Collecting Data 1.3 Types of Data 1.4 Methods of Data Analysis Recommended Reading 2 Introduction to MATLAB 2.1 MATLAB in Earth Sciences 2.2 Getting Started 2.3 The Syntax 2.4 Data Storage 2.5 Data Handling 2.6 Scripts and Functions 2.7 Basic Visualization Tools Recommended Reading 3 Univariate Statistics 3.1 Introduction 3.2 Empirical Distributions Measures of Central Tendency Measures of Dispersion 3.3 Example of Empirical Distributions 3.4 Theoretical Distributions Uniform Distribution Binomial or Bernoulli Distribution Poisson Distribution Normal or Gaussian Distribution Logarithmic Normal or Log-Normal Distribution Student's t Distribution Fisher's F Distribution Χ2 or Chi-Squared Distribution 3.5 Example ofTheoretical Distributions 3.6 Thet-Test 3.7 TheF-Test 3.8 The Χ2-Test Recommended Reading 4 Bivariate Statistics 4.1 Introduction 4.2 Pearson's Correlation Coefficient 4.3 Classical Linear Regression Analysis and Prediction 4.4 Analyzing the Residuals 4.5 Bootstrap Estimates of the Regression Coefficients 4.6 Jackknife Estimates of the Regression Coefficients 4.7 Cross Validation 4.8 Reduced Major Axis Regression 4.9 Curvilinear Regression Recommended Reading 5 Time-Series Analysis 5.1 Introduction 5.2 Generating Signals 5.3 Blackman-Tukey Autospectral Analysis 5.4 Blackman-Tukey Crossspectral Analysis 5.5 Interpolating and Analyzing Unevenly-Spaced Data 5.6 Evolutionary Blackman-Tukey Powerspectrum 5.7 Lomb-Scargle Powerspectrum 5.8 Wavelet Powerspectrum 5.9 Nonlinear Time-Series Analysis (by N. Marwarn) Phase Space Portrait Recurrence Plots Recommended Reading 6 Signal Processing 6.1 Introduction 6.2 Generating Signals 6.3 Linear Time-Invariant Systems 6.4 Convolution and Filtering 6.5 Comparing Functions for Filtering Data Series 6.6 Recursive and Nonrecursive Filters 6.7 Impulse Response 6.8 Frequency Response 6.9 Filter Design 6.10 Adaptive Filtering Recommended Reading 7 Spatial Data 7.1 Types of Spatial Data 7.2 The GSHHS Shoreline Data Set 7.3 The 2-Minute Gridded Global Elevation Data ETOPO2 7.4 The 30-Arc Seconds Elevation Model GTOPO30 7.5 The Shuttle Radar Topography Mission SRTM 7.6 Gridding and Contouring Background 7.7 Gridding Example 7.8 Comparison of Methods and Potential Artifacts 7.9 Statistics of Point Distributions Test for Uniform Distribution Test for Random Distribution Test for Clustering 7.10 Analysis of Digital Elevation Models (by R. Gebbers) 7.11 Geostatistics and Kriging (by R. Gebbers) Theorical Background Preceding Analysis Variography with the Classical Variogram Kriging Discussion of Kriging Recommended Reading 8 Image Processing 8.1 Introduction 8.2 Datastorage 8.3 Importing, Processing and Exporting Images 8.4 Importing, Processing and Exporting Satellite Images 8.5 Georeferencing Satellite Images 8.6 Digitizing from the Screen Recommended Reading 9 Multivariate Statistics 9.1 Introduction 9.2 Principal Component Analysis 9.3 Independent Component Analysis (by N. Marwan) 9.4 Cluster Analysis Recommended Reading 10 Statistics on Directional Data 10.1 Introduction 10.2 Graphical Representation 10.3 Empirical Distributions 10.4 Theoretical Distributions 10.5 Test for Randomness of Directional Data 10.6 Test for the Significance of a Mean Direction 10.7 Test for the Difference of Two Sets of Directions Recommended Reading General Index

Note: Erscheinungsjahr in Vorlageform:2007

Note: Die Vorlage enth. insgesamt 19 Werke

Note: Inhalt: 1 Einleitung. - 1.1 Alltägliche Probleme. - 1.2 Uni- und multivariate Daten. - 1.3 Wege ins Statistiklabyrinth. - 2 Statistische Grundlagen. - 2.1 Einführung in die Terminologie. - 2.2 Datentypen -Skalenniveaus. - 2.3 Korrelation. - 2.4 Regression. - 2.5 Lineare Regression. - 2.6 Multiplelineare Regression. - 2.7 Unimodale Modelle - die Gauß'sche Regression. - 2.8 Logistische und Gauß'sche logistische Regression. - 2.9 Interaktionen. - 2.10 Gewichtetes Mittel. - 2.11 Partielle Analysen. - 3 Datenmanipulationen. - 3.1 Normalverteilung und Transformationen. - 3.2 Standardisierungen. - 3.3 Transponieren, Umkodieren und Maskieren. - 4 Ähnlichkeits- und Distanzmaße. - 4.1 Qualitative Ähnlichkeitsmaße. - 4.2 Quantitative Ähnlichkeitsmaße. - 4.3 Distanzmaße. - 4.4 Vergleich der geschilderten Koeffizienten. - 5 Ordinationen - das Prinzip. - 5.1 Dimensionsreduktion als Analysestrategie. - 5.2 Polare Ordination. - 6 Korrespondenzanalyse (CA). - 6.1 Das Prinzip. - 6.2 Mathematische Artefakte - Probleme der CA. - 6.3 DCA {Detrended Correspondence Analysis). - 6.4 Zusammenfassendes zu Problemen der CA und DCA. - 7 Interpretation von CA und DCA. - 7.1 Zur Skalierung und Interpretation der Ordinationsdiagramme. - 7.2 Umweltvariablen-Interaktionen von Effekten. - 7.3 Ordination und Umweltdaten. - 8 Kanonische Ordination (constrained ordination). - 8.1 Prinzip der Kanonischen Korrespondenzanalyse (CCA). - 8.2 Interpretation eines CCA-Diagramms. - 8.3 Forward selection bei kanonischen Ordinationen. - 8.4 Überprüfung einer CCA. - 9 Hauptkomponentenanalyse (PCA). - 9.1 Das Prinzip - geometrische Herleitung. - 9.2 Das Prinzip - der mathematische Ansatz. - 9.3 Optionen bei einer PCA. - 9.4 Stärken und Schwächen der PCA. - 9.5 Faktorenanalyse. - 10 Lineare Methoden und Umweltdaten: PCA und RDA. - 10.1 Indirekte Ordination. - 10.2 Kanonische Ordination - Prinzip der Redundanzanalyse. - 10.3 Interpretation einer RDA. - 11 Partielle Ordination und variance partitioning. - 11.1 Kovariablen. - 11.2 Partielle PCA, CA, DCA. - 11.3 Partielle kanonische Ordination. - 11.4 Variance partitioning. - 12 Multidimensionale Skalierung. - 12.1 Der andere Weg zum Ziel. - 12.2 Metrische Multidimensionale Skalierung - Hauptkoordinatenanalyse. - 12.3 Nichtmetrische Multidimensionale Skalierung. - 12.3.1 Das Prinzip. - 12.3.2 NMDS - Optionen und Probleme. - 12.3.3 Ablauf einer NMDS. - 13 Klassifikation - das Prinzip. - 13.1 Das Wesen von Klassifikationen. - 13.2 Die wichtigsten Klassifikationsstrategien. - 14 Agglomerative Klassifikationsverfahren. - 14.1Clusteranalyse - Grundlagen. - 14.2 Auswertung von Dendrogrammen. - 15 Divisive Klassifikationsverfahren. - 15.1 Ordination Space Partitioning. - 15.2 TWINSPAN. - 15.3 Ablauf einer TWINSPAN-Analyse. - 15.4 Kritik an der TWINSPAN-Analyse. - 16 Sonstige Verfahren zur Beschreibung von Gruppenstrukturen. - 16.1 Nichthierarchische agglomerative Verfahren. - 16.2 Nichthierarchische divisive Verfahren. - 16.3 Numerische "treue"-basierte Verfahren. - 16.4 Diskriminanzanalyse. - 16.4.1 Das Prinzip. - 16.4.2 Voraussetzungen. - 16.4.3 Gütekriterien/Prüfung der Ergebnisse. - 17 Permutationsbasierte Tests. - 17.1 Das Prinzip von Permutationstests. - 17.2 Test auf Signifikanz von Ordinationsachsen. - 17.3 Mantel-Test. - 17.4 Gruppenvergleiche - Mantel-Tests und MRPP. - 17.5 Procrustes-Analysen. - 17.6 Indicator Species Analysis. - 17.7 Ausblick Randomisierungsverfahren. - Literatur. - Sachverzeichnis.

Note: Contents 1. Introduction 1.1 Historical Background 1.2 Some Examples of Spectral Methods 1.2.1 A Fourier Galerkin Method for the Wave Equation 1.2.2 A Chebyshev Collocation Method for the Heat Equation 1.2.3 A Legendre Galerkin with Numerical Integration (G-NI) Method for the Advection-Diffusion-Reaction Equation 1.2.4 A Legendre Tau Method for the Poisson Equation 1.2.5 Basic Aspects of Galerkin, Collocation, G-NI and Tau Methods 1.3 Three-Dimensional Applications in Fluids: A Look Ahead 2. Polynomial Approximation 2.1 The Fourier System 2.1.1 The Continuous Fourier Expansion 2.1.2 The Discrete Fourier Expansion 2.1.3 Differentiation 2.1.4 The Gibbs Phenomenon 2.2 Orthogonal Polynomials in (−1, 1) 2.2.1 Sturm-Liouville Problems 2.2.2 Orthogonal Systems of Polynomials 2.2.3 Gauss-Type Quadratures and Discrete Polynomial Transforms 2.3 Legendre Polynomials 2.3.1 Basic Formulas 2.3.2 Differentiation 2.3.3 Orthogonality, Diagonalization and Localization 2.4 Chebyshev Polynomials 2.4.1 Basic Formulas 2.4.2 Differentiation 2.5 Jacobi Polynomials 2.6 Approximation in Unbounded Domains 2.6.1 Laguerre Polynomials and Laguerre Functions 2.6.2 Hermite Polynomials and Hermite Functions 2.7 Mappings for Unbounded Domains 2.7.1 Semi-Infinite Intervals 2.7.2 The Real Line 2.8 Tensor-Product Expansions 2.8.1 Multidimensional Mapping 2.9 Expansions on Triangles and Related Domains 2.9.1 Collapsed Coordinates and Warped Tensor-Product Expansions 2.9.2 Non-Tensor-Product Expansions 2.9.3 Mappings 3. Basic Approaches to Constructing Spectral Methods 3.1 Burgers Equation 3.2 Strong and Weak Formulations of Differential Equations 3.3 Spectral Approximation of the Burgers Equation 3.3.1 Fourier Galerkin 3.3.2 Fourier Collocation 3.3.3 Chebyshev Tau 3.3.4 Chebyshev Collocation 3.3.5 Legendre G-NI 3.4 Convolution Sums 3.4.1 Transform Methods and Pseudospectral Methods 3.4.2 Aliasing Removal by Padding or Truncation 3.4.3 Aliasing Removal by Phase Shifts 3.4.4 Aliasing Removal for Orthogonal Polynomials 3.5 Relation Between Collocation, G-NI and Pseudospectral Methods 3.6 Conservation Forms 3.7 Scalar Hyperbolic Problems 3.7.1 Enforcement of Boundary Conditions 3.7.2 Numerical Examples 3.8 Matrix Construction for Galerkin and G-NI Methods 3.8.1 Matrix Elements 3.8.2 An Example of Algebraic Equivalence between G-NI and Collocation Methods 3.9 Polar Coordinates 3.10 Aliasing Effects 4. Algebraic Systems and Solution Techniques 4.1 Ad-hoc Direct Methods 4.1.1 Fourier Approximations 4.1.2 Chebyshev Tau Approximations 4.1.3 Galerkin Approximations 4.1.4 Schur Decomposition and Matrix Diagonalization 4.2 Direct Methods 4.2.1 Tensor Products of Matrices 4.2.2 Multidimensional Stiffness and Mass Matrices 4.2.3 Gaussian Elimination Techniques 4.3 Eigen-Analysis of Spectral Derivative Matrices 4.3.1 Second-Derivative Matrices 4.3.2 First-Derivative Matrices 4.3.3 Advection-Diffusion Matrices 4.4 Preconditioning 4.4.1 Fundamentals of Iterative Methods for Spectral Discretizations 4.4.2 Low-Order Preconditioning of Model Spectral Operators in One Dimension 4.4.3 Low-Order Preconditioning in Several Dimensions 4.4.4 Spectral Preconditioning 4.5 Descent and Krylov Iterative Methods for Spectral Equations 4.5.1 Multidimensional Matrix-Vector Multiplication 4.5.2 Iterative Methods 4.6 Spectral Multigrid Methods 4.6.1 One-Dimensional Fourier Multigrid Model Problem 4.6.2 General Spectral Multigrid Methods 4.7 Numerical Examples of Direct and Iterative Methods 4.7.1 Fourier Collocation Discretizations 4.7.2 Chebyshev Collocation Discretizations 4.7.3 Legendre G-NI Discretizations 4.7.4 Preconditioners for Legendre G-NI Matrices 4.8 Interlude 5. Polynomial Approximation Theory 5.1 Fourier Approximation 5.1.1 Inverse Inequalities for Trigonometric Polynomials 5.1.2 Estimates for the Truncation and Best Approximation Errors 5.1.3 Estimates for the Interpolation Error 5.2 Sturm-Liouville Expansions 5.2.1 Regular Sturm-Liouville Problems 5.2.2 Singular Sturm-Liouville Problems 5.3 Discrete Norms 5.4 Legendre Approximations 5.4.1 Inverse Inequalities for Algebraic Polynomials 5.4.2 Estimates for the Truncation and Best Approximation Errors 5.4.3 Estimates for the Interpolation Error 5.4.4 Scaled Estimates 5.5 Chebyshev Approximations 5.5.1 Inverse Inequalities for Polynomials 5.5.2 Estimates for the Truncation and Best Approximation Errors 5.5.3 Estimates for the Interpolation Error 5.6 Proofs of Some Approximation Results 5.7 Other Polynomial Approximations 5.7.1 Jacobi Polynomials 5.7.2 Laguerre and Hermite Polynomials 5.8 Approximation in Cartesian-Product Domains 5.8.1 Fourier Approximations 5.8.2 Legendre Approximations 5.8.3 Mapped Operators and Scaled Estimates 5.8.4 Chebyshev and Other Jacobi Approximations 5.8.5 Blended Trigonometric and Algebraic Approximations 5.9 Approximation in Triangles and Related Domains 6. Theory of Stability and Convergence 6.1 Three Elementary Examples Revisited 6.1.1 A Fourier Galerkin Method for the Wave Equation 6.1.2 A Chebyshev Collocation Method for the Heat Equation 6.1.3 A Legendre Tau Method for the Poisson Equation 6.2 Towards a General Theory 6.3 General Formulation of Spectral Approximations to Linear Steady Problems 6.4 Galerkin, Collocation, G-NI and Tau Methods 6.4.1 Galerkin Methods 6.4.2 Collocation Methods 6.4.3 G-NI Methods 6.4.4 Tau Methods 6.5 General Formulation of Spectral Approximations to Linear Evolution Problems 6.5.1 Conditions for Stability and Convergence: The Parabolic Case 6.5.2 Conditions for Stability and Convergence: The Hyperbolic Case 6.6 The Error Equation 7. Analysis of Model Boundary-Value Problems 7.1 The Poisson Equation 7.1.1 Legendre Methods 7.1.2 Chebyshev Methods 7.1.3 Other Boundary-Value Problems 7.2 Singularly Perturbed Elliptic Equations 7.2.1 Stabilization of Spectral Methods 7.3 The Eigenvalues of Some Spectral Operators 7.3.1 The Discrete Eigenvalues for Lu = −uxx 7.3.2 The Discrete Eigenvalues for Lu = −νuxx + βux 7.3.3 The Discrete Eigenvalues for Lu = ux 7.4 The Preconditioning of Spectral Operators 7.5 The Heat Equation 7.6 Linear Hyperbolic Equations 7.6.1 Periodic Boundary Conditions 7.6.2 Nonperiodic Boundary Conditions 7.6.3 The Resolution of the Gibbs Phenomenon 7.6.4 Spectral Accuracy for Non-Smooth Solutions 7.7 Scalar Conservation Laws 7.8 The Steady Burgers Equation Appendix A. Basic Mathematical Concepts A.1 Hilbert and Banach Spaces A.2 The Cauchy-Schwarz Inequality A.3 Linear Operators Between Banach Spaces A.4 The Fr´echet Derivative of an Operator A.5 The Lax-Milgram Theorem A.6 Dense Subspace of a Normed Space A.7 The Spaces Cm(Ω), m ≥ 0 A.8 Functions of Bounded Variation and the Riemann(-Stieltjes) Integral A.9 The Lebesgue Integral and Lp-Spaces A.10 Infinitely Differentiable Functions and Distributions A.11 Sobolev Spaces and Sobolev Norms A.12 The Sobolev Inequality A.13 The Poincar´e Inequality A.14 The Hardy Inequality A.15 The Gronwall Lemma Appendix B. Fast Fourier Transforms Appendix C. Iterative Methods for Linear Systems C.1 A Gentle Approach to Iterative Methods C.2 Descent Methods for Symmetric Problems C.3 Krylov Methods for Nonsymmetric Problems Appendix D. Time Discretizations D.1 Notation and Stability Definitions D.2 Standard ODE Methods D.2.1 Leap Frog Method D.2.2 Adams-Bashforth Methods D.2.3 Adams-Moulton Methods D.2.4 Backwards-Difference Formulas D.2.5 Runge-Kutta Methods D.3 Integrating Factors D.4 Low-Storage Schemes References Index

Note: Contents Theme 1 History of Antarctic Research 1.1 The Road to Gondwana via the Early SCAR Symposia / A. B. Ford 1.2 Exploring the Unknown: History of the First German South Polar Expedition 1901–1903 / C. Lüdecke Theme 2 Antarctica – The Old Core 2.1 Characteristics of Metamorphosed Banded Iron Formation and Its Relation to the Magnetic Anomaly in the Mt. Riiser-Larsen Area, Amundsen Bay, Enderby Land, Antarctica / M. Funaki, P. Dolinsky, N. Ishikawa, A. Yamazaki 2.2 Experimental Constraints on the Decompressional P-T Paths of Rundvågshetta Granulites, Lützow-Holm Complex, East Antarctica / T. Kawasaki, Y. Motoyoshi 2.3 Sapphirine – Orthopyroxene – Garnet Granulite from Schirmacher Hills, Central Dronning Maud Land / S. Baba, M. Owada, E. S. Grew, K. Shiraishi 2.4 Genesis of Ferropotassic A-Type Granitoids of Mühlig-Hofmannfjella, Central Dronning Maud Land, East Antarctica / M. J. D’Souza, A. V. K. Prasad, R. Ravindra 2.5 Late Pan-African Fluid Infiltration in the Mühlig-Hofmann- and Filchnerfjella of Central Dronning Maud Land, East Antarctica / A. K. Engvik, S. Elvevold 2.6 Electron Microprobe (EMP) Dating on Monazite from Forefinger Point Granulites, East Antarctica: Implication for Pan-African Overprint / Y. Motoyoshi, T. Hokada, K. Shiraishi 2.7 Tectonic Subdivision of the Prince Charles Mountains: A Review of Geologic and Isotopic Data / E. V. Mikhalsky, A. A. Laiba, B. V. Beliatsky 2.8 Crustal Provinces of the Prince Charles Mountains Region and Surrounding Areas in the Light of Aeromagnetic Data / A. V. Golynsky, V. N. Masolov, V. S. Volnukhin, D. A. Golynsky 2.9 Magnetic Anomalies of the Grove Mountains Region and Their Geological Significance / A. V. Golynsky, D. A. Golynsky, V. N. Masolov, V. S. Volnukhin Theme 3 The Continent Beneath the Ice 3.1 ADMAP – A Digital Magnetic Anomaly Map of the Antarctic / A. V. Golynsky, M. Chiappini, D. Damaske, F. Ferraccioli, C. A. Finn, T. Ishihara, H. R. Kim, L. Kovacs, V. N. Masolov, P. Morris, R. von Frese 3.2 Identifying Major Sedimentary Basins Beneath the West Antarctic Ice Sheet from Aeromagnetic Data Analysis / R. E. Bell, M. Studinger, G. Karner, C. A. Finn, D. D. Blankenship 3.3 Bedrock Plateaus within the Ross Embayment and beneath the West Antarctic Ice Sheet, Formed by Marine Erosion in Late Tertiary Time / D. S. Wilson, B. P. Luyendyk 3.4 Inversion of Airborne Gravity Data Acquired over Subglacial Lakes in East Antarctica / I. Y. Filina, D. D. Blankenship, L. Roy, M. K. Sen, T. G. Richter, J. W. Holt 3.5 Russian Geophysical Studies of Lake Vostok, Central East Antarctica / V. N. Masolov, S. V. Popov, V. V. Lukin, A. N. Sheremetyev, A. M. Popkov 3.6 Morphology of the Subglacial Bed Relief of Lake Vostok Basin Area (Central East Antarctica) Based on RES and Seismic Data / S. V. Popov, A. N. Lastochkin, V. N. Masolov, A. M. Popkov 3.7 Deep Reflection Imaging beneath the Mizuho Plateau, East Antarctica, by SEAL-2002 Seismic Experiment / M. Yamashita, H. Miyamachi, M. Kanao, T. Matsushima, S. Toda, M. Takada, A. Watanabe 3.8 Seismic Anisotropy beneath Northern Victoria Land from SKS Splitting Analysis / S. Pondrelli, L. Margheriti, S. Danesi Theme 4 Gondwana Margins in Antarctica 4.1 Scouting Craton’s Edge in Paleo-Pacific Gondwana / C. A. Finn, J. W. Goodge, D. Damaske, C. M. Fanning 4.2 The Matusevich Fracture Zone in Oates Land, East Antarctica / G. Kleinschmidt, A. L. Läufer 4.3 Tectonic Model for Development of the Byrd Glacier Discontinuity and Surrounding Regions of the Transantarctic Mountains during the Neoproterozoic – Early Paleozoic / E. Stump, B. Gootee, F. Talarico 4.4 Depositional Environments of the Byrd Group, Byrd Glacier Area: A Cambrian Record of Sedimentation, Tectonism, and Magmatism / B. Gootee, E. Stump 4.5 Late-Ross Structures in the Wilson Terrane in the Rennick Glacier Area (Northern Victoria Land, Antarctica) / A. L. Läufer, G. Kleinschmidt, F. Rossetti 4.6 Style of Uplift of Paleozoic Terranes in Northern Victoria Land, Antarctica: Evidence from K-Ar Age Patterns / C. J. Adams Theme 5 Antarctic Peninsula Active Margin Tectonics 5.1 Patagonia – Antarctica Connections before Gondwana Break-Up / F. Hervé, H. Miller, C. Pimpirev 5.2 Moho Depth along the Antarctic Peninsula and Crustal Structure across the Landward Projection of the Hero Fracture Zone / T. Janik, P. Þroda, M. Grad, A. Guterch 5.3 Crustal Thinning and the Development of Deep Depressions at the Scotia- Antarctic Plate Boundary (Southern Margin of Discovery Bank, Antarctica) / J. Galindo-Zaldívar, J. C. Balanyá, F. Bohoyo, A. Jabaloy, A. Maldonado, J. M. Martínez-Martínez, J. Rodríguez-Fernández, E. Suriñach 5.4 Bransfield Basin Tectonic Evolution / J. Galindo-Zaldívar, L. Gamboa , A. Maldonado, S. Nakao, Y. Bochu 5.5 The Sedimentary Sequences of Hurd Peninsula, Livingston Island, South Shetland Islands: Part of the Late Jurassic–Cretaceous Depositional History of the Antarctic Peninsula / C. Pimpirev, K. Stoykova, M. Ivanov, D. Dimov 5.6 Regional Structures and Geodynamic Evolution of North Greenwich (Fort Williams Point) and Dee Islands, South Shetland Islands / J. F. Dumont, E. Santana, F. Hervé, C. Zapata 5.7 The Eocene Volcaniclastic Sejong Formation, Barton Peninsula, King George Island, Antarctica: Evolving Arc Volcanism from Precursory Fire Fountaining to Vulcanian Eruptions / S. B. Kim, Y. K. Sohn, M. Y. Choe 5.8 Elephant Island Recent Tectonics in the Framework of the Scotia-Antarctic-South Shetland Block Triple Junction (NE Antarctic Peninsula) / J. Galindo-Zaldívar, A. Maestro, J. López-Martínez, C. S. de Galdeano 5.9 Tectonics and Geomorphology of Elephant Island, South Shetland Islands / J. López-Martínez, R. A. J. Trouw, J. Galindo-Zaldívar, A. Maestro, L. S. A. Simões, F. F. Medeiros, C. C. Trouw 5.10 Geodynamical Studies on Deception Island: DECVOL and GEODEC Projects / M. Berrocoso, A. García-García, J. Martín-Dávila, M. Catalán-Morollón, M. Astiz, M. E. Ramírez, C. Torrecillas, J. M. E. de Salamanca Theme 6 Antarctic Rift Tectonics 6.1 Mawson Breccias Intrude Beacon Strata at Allan Hills, South Victoria Land: Regional Implications / D. H. Elliot, E. H. Fortner, C. B. Grimes 6.2 What Supports the Marie Byrd Land Dome? An Evaluation of Potential Uplift Mechanisms in a Continental Rift System / W. E. LeMasurier 6.3 A Multi-Phase Rifting Model for the Victoria Land Basin, Western Ross Sea / F. J. Davey, L. De Santis 6.4 Rift History of the Western Victoria Land Basin: A new Perspective Based on Integration of Cores with Seismic Reflection Data / C. R. Fielding, S. A. Henrys, T. J. Wilson 6.5 Constraints on the Timing of Extension in the Northern Basin, Ross Sea / S. C. Cande, J. M. Stock 6.6 The Structure of the Continental Margin off Wilkes Land and Terre Adélie Coast, East Antarctica / J. B. Colwell, H. M. J. Stagg, N. G. Direen, G. Bernardel, I. Borissova 6.7 Post-Rift Continental Slope and Rise Sediments from 38° E to 164° E, East Antarctica / P. E. O’Brien, S. Stanley, R. Parums Theme 7 Antarctic Neotectonics, Observatories and Data Bases 7.1 On Seismic Strain-Release within the Antarctic Plate / A. M. Reading 7.2 Vertical Crustal Deformation in Dronning Maud Land, Antarctica: Observation versus Model Prediction / M. Scheinert, E. Ivins, R. Dietrich, A. Rülke 7.3 Seismic Activity Associated with Surface Environmental Changes of the Earth System, around Syowa Station, East Antarctica / M. Kanao, K. Kaminuma 7.4 Geodynamic Features and Density Structure of the Earth’s Interior of the Antarctic and Surrounded Regions with the Gravimetric Tomography Method / R. Kh. Greku, V. P. Usenko, T. R. Greku 7.5 Some Recent Characteristics of Geomagnetic Secular Variations in Antarctica / A. Meloni, L. R. Gaya-Piqué, P. De Michelis, A. De Santis 7.6 Topographic and Geodetic Research by GPS, Echosounding and ERS Altimetric, and SAR Interferometric Surveys during Ukrainian Antarctic Expeditions in the West Antarctic / R. Greku, G. Milinevsky, Y. Ladanovsky, P. Bahmach, T. Greku 7.7 Geodetic Research o