ALBERT

Note: Contents: Preface to the Second Edition. - Preface to the First Edition. - Legal Matters. - Computer Programs by Chapter and Section. - 1 Preliminaries. - 1.0 Introduction. - 1.1 Program Organization and Control Structures. - 1.2 Error, Accuracy, and Stability. - 2 Solution of Linear Algebraic Equations. - 2.0 Introduction. - 2.1 Gauss-Jordan Elimination. - 2.2 Gaussian Elimination with Backsubstitution. - 2.3 LU Decomposition and Its Applications. - 2.4 Tridiagonal and Band Diagonal Systems of Equations. - 2.5 Iterative Improvement of a Solution to Linear Equations. - 2.6 Singular Value Decomposition. - 2.7 Sparse Linear Systems. - 2.8 Vandermonde Matrices and Toeplitz Matrices. - 2.9 Cholesky Decomposition. - 2.10 QR Decomposition. - 2.11 Is Matrix Inversion an N3 Process?. - 3 Interpolation and Extrapolation. - 3.0 Introduction. - 3.1 Polynomial Interpolation and Extrapolation. - 3.2 Rational Function Interpolation and Extrapolation. - 3.3 Cubic Spline Interpolation. - 3.4 How to Search an Ordered Table. - 3.5 Coefficients of the Interpolating Polynomial. - 3.6 Interpolation in Two or More Dimensions. - 4 Integration of Functions. - 4.0 Introduction. - 4.1 Classical Formulas for Equally Spaced Abscissas. - 4.2 Elementary Algorithms. - 4.3 Romberg Integration. - 4.4 Improper Integrals. - 4.5 Gaussian Quadratures and Orthogonal Polynomials. - 4.6 Multidimensional Integrals. - 5 Evaluation of Functions. - 5.0 Introduction. - 5.1 Series and Their Convergence. - 5.2 Evaluation of Continued Fractions. - 5.3 Polynomials and Rational Functions. - 5.4 Complex Arithmetic. - 5.5 Recurrence Relations and Clenshaw's Recurrence Formula. - 5.6 Quadratic and Cubic Equations. - 5.7 Numerical Derivatives. - 5.8 Chebyshev Approximation. - 5.9 Derivatives or Integrals of a Chebyshev-approximated Function. - 5.10 Polynomial Approximation from Chebyshev Coefficients. - 5.11 Economization of Power Series. - 5.12 Pade Approximants. - 5.13 Rational Chebyshev Approximation. - 5.14 Evaluation of Functions by Path Integration. - 6 Special Functions. - 6.0 Introduction. - 6.1 Gamma Function, Beta Function, Factorials, Binomial Coefficients. - 6.2 Incomplete Gamma Function, Error Function, Chi-Square Probability Function, Cumulative Poisson Function. - 6.3 Exponential Integrals. - 6.4 Incomplete Beta Function, Student's Distribution, F-Distribution, Cumulative Binomial Distribution. - 6.5 Bessel Functions of Integer Order. - 6.6 Modified Bessel Functions of Integer Order. - 6.7 Bessel Functions of Fractional Order, Airy Functions, Spherical Bessel Functions. - 6.8 Spherical Harmonics. - 6.9 Fresnel Integrals, Cosine and Sine Integrals. - 6.10 Dawson's Integral. - 6.11 Elliptic Integrals and Jacobian Elliptic Functions. - 6.12 Hypergeometric Functions. - 7 Random Numbers. - 7.0 Introduction. - 7.1 Uniform Deviates. - 7.2 Transformation Method: Exponential and Normal Deviates. - 7.3 Rejection Method: Gamma, Poisson, Binomial Deviates. - 7.4 Generation of Random Bits. - 7.5 Random Sequences Based on Data Encryption. - 7.6 Simple Monte Carlo Integration. - 7.7 Quasi- (that is, Sub-) Random Sequences. - 7.8 Adaptive and Recursive Monte Carlo Methods. - 8 Sorting. - 8.0 Introduction. - 8.1 Straight Insertion and Shell's Method. - 8.2 Quicksort. - 8.3 Heapsort. - 8.4 Indexing and Ranking. - 8.5 Selecting the Mth Largest. - 8.6 Determination of Equivalence Classes. - 9 Root Finding and Nonlinear Sets of Equations. - 9.0 Introduction. - 9.1 Bracketing and Bisection. - 9.2 Secant Method, False Position Method, and Ridders' Method. - 9.3 Van Wijngaarden-Dekker-Brent Method. - 9.4 Newton-Raphson Method Using Derivative. - 9.5 Roots of Polynomials. - 9.6 Newton-Raphson Method for Nonlinear Systems of Equations. - 9.7 Globally Convergent Methods for Nonlinear Systems of Equations. - 10 Minimization or Maximization of Functions. - 10.0 Introduction. - 10.1 Golden Section Search in One Dimension. - 10.2 Parabolic Interpolation and Brent's Method in One Dimension. - 10.3 One-Dimensional Search with First Derivatives. - 10.4 Downhill Simplex Method in Multidimensions. - 10.5 Direction Set (Powell's) Methods in Multidimensions. - 10.6 Conjugate Gradient Methods in Multidimensions. - 10.7 Variable Metric Methods in Multidimensions. - 10.8 Linear Programming and the Simplex Method. - 10.9 Simulated Annealing Methods. - 11 Eigensystems. - 11.0 Introduction. - 11.1 Jacobi Transformations of a Symmetric Matrix. - 11.2 Reduction of a Symmetric Matrix to Tridiagonal Form: Givens and Householder Reductions. - 11.3 Eigenvalues and Eigenvectors of a Tridiagonal Matrix. - 11.4 Hermitian Matrices. - 11.5 Reduction of a General Matrix to Hessenberg Form. - 11.6 The QR Algorithm for Real Hessenberg Matrices. - 11.7 Improving Eigenvalues and/or Finding Eigenvectors by Inverse Iteration. - 12 Fast Fourier Transform. - 12.0 Introduction. - 12.1 Fourier Transform of Discretely Sampled Data. - 12.2 Fast Fourier Transform (FFT). - 12.3 FFT of Real Functions, Sine and Cosine Transforms. - 12.4 FFT in Two or More Dimensions. - 12.5 Fourier Transforms of Real Data in Two and Three Dimensions. - 12.6 External Storage or Memory-Local FFTs. - 13 Fourier and Spectral Applications. - 13.0 Introduction. - 13.1 Convolution and Deconvolution Using the FFT. - 13.2 Correlation and Autocorrelation Using the FFT. - 13.3 Optimal (Wiener) Filtering with the FFT. - 13.4 Power Spectrum Estimation Using the FFT. - 13.5 Digital Filtering in the Time Domain. - 13.6 Linear Prediction and Linear Predictive Coding. - 13.7 Power Spectrum Estimation by the Maximum Entropy (All Poles) Method. - 13.8 Spectral Analysis of Unevenly Sampled Data. - 13.9 Computing Fourier Integrals Using the FFT. - 13.10 Wavelet Transforms. - 13.11 Numerical Use of the Sampling Theorem. - 14 Statistical Description of Data. - 14.0 Introduction. - 14.1 Moments of a Distribution: Mean, Variance, Skewness, and So Forth. - 14.2 Do Two Distributions Have the Same Means or Variances?. - 14.3 Are Two Distributions Different?. - 14.4 Contingency Table Analysis of Two Distributions. - 14.5 Linear Correlation. - 14.6 Nonparametric or Rank Correlation. - 14.7 Do Two-Dimensional Distributions Differ?. - 14.8 Savitzky-Golay Smoothing Filters. - 15 Modeling of Data. - 15.0 Introduction. - 15.1 Least Squares as a Maximum Likelihood Estimator. - 15.2 Fitting Data to a Straight Line. - 15.3 Straight-Line Data with Errors in Both Coordinates. - 15.4 General Linear Least Squares. - 15.5 Nonlinear Models. - 15.6 Confidence Limits on Estimated Model Parameters. - 15.7 Robust Estimation. - 16 Integration of Ordinary Differential Equations. - 16.0 Introduction. - 16.1 Runge-Kutta Method. - 16.2 Adaptive Stepsize Control for Runge-Kutta. - 16.3 Modified Midpoint Method. - 16.4 Richardson Extrapolation and the Bulirsch-Stoer Method. - 16.5 Second-Order Conservative Equations. - 16.6 Stiff Sets of Equations. - 16.7 Multistep, Multivalue, and Predictor-Corrector Methods. - 17 Two Point Boundary Value Problems. - 17.0 Introduction. - 17.1 The Shooting Method. - 17.2 Shooting to a Fitting Point. - 17.3 Relaxation Methods. - 17.4 A Worked Example: Spheroidal Harmonics. - 17.5 Automated Allocation of Mesh Points. - 17.6 Handling Internal Boundary Conditions or Singular Points. - 18 Integral Equations and Inverse Theory. - 18.0 Introduction. - 18.1 Fredholm Equations of the Second Kind. - 18.2 Volterra Equations. - 18.3 Integral Equations with Singular Kernels. - 18.4 Inverse Problems and the Use of A Priori Information. - 18.5 Linear Regularization Methods. - 18.6 Backus-Gilbert Method. - 18.7 Maximum Entropy Image Restoration. - 19 Partial Differential Equations. - 19.0 Introduction. - 19.1 Flux-Conservative Initial Value Problems. - 19.2 Diffusive Initial Value Problems. - 19.3 Initial Value Problems in Multidi

Note: Contents Preface Acknowledgements 1 Introduction 1.1 Glacier forelands and simplicity 1.2 Ecology and primary succession 1.3 Space-for-time substitution (chronosequences) 1.4 Geoecology (landscape ecology) 2 The nature of the timescale 2.1 Glacier variations 2.2 Dating techniques 2.2.1 Historical sources 2.2.2 Biological dating 2.2.3 Physico-chemical dating 2.3 Terrain age sequences and areal chronologies 3 The physical landscape 3.1 The legacy of glaciation 3.1.1 Glacial erosion 3.1.2 Glacial sediments 3.1.3 Depositional landforms and landsystems 3.2 Proglacial landscape modification 3.2.1 Glacio-fluvial activity 3.2.2 Consolidation and slope stabilization 3.2.3 Pervection 3.2.4 Cryogenic processes: frost weathering 3.2.5 Frost-heave and frost-sorting 3.2.6 Solifluction and other periglacial slope processes 3.2.7 Nivation 3.2.8 Aeolian processes 3.3 The climatic environment 3.3.1 Regional climate 3.3.2 Meso-scale climatic gradients 3.3.3 Microclimate 3.3.4 Climatic change 3.4 Spatial variation and change in the physical landscape 3.4.1 Spatial patterns at various scales 3.4.2 Physical processes and landscape change 4 Soil development 4.1 Soil chronosequences and chronofunctions 4.1.1 Conceptual framework 4.1.2 An example: Glacier Bay, Alaska 4.2 Soil properties and pedogenic processes 4.2.1 Texture 4.2.2 Micromorphology 4.2.3 Organic content 4.2.4 pH and base status 4.2.5 Iron and aluminium 4.2.6 Chemical weathering processes 4.2.7 Nitrogen 4.2.8 Phosphorus 4.3 Environmental controls on pedogenesis 4.3.1 Parent material 4.3.2 Topography 4.3.3 Biota 4.3.4 Climatic controls 4.4 Soil formation in time and space 4.4.1 Soil development and equilibrium concepts 4.4.2 Spatial variation and soil chronosequences 5 Plant succession: patterns and environmental factors 5.1 Vegetational chronosequences: methodological considerations 5.1.1 Concept and limitations 5.1.2 Tests of chronoseauences: observed successions 5.1.3 Tests of chronosequences: retrospective analysis 5.2 Inferred successional trends 5.2.1 Cover 5.2.2 Spatial organization 5.2.3 Stratification and physiognomy 5.2.4 Biomass 5.2.5 Species diversity 5.2.6 Species composition and successional stages 5.2.7 Population attributes and physiological traits 5.3 Spatial variation and successional pathways 5.3.1 Within-foreland patterns: mapping 5.3.2 Quantitative community analysis at Storbreen, Jotunheimen 5.3.3 Inferred successional pathways elsewhere 5.3.4 Between-foreland patterns: a comparative approach 5.4 Environmental controls on successional sequences 5.4.1 Initial site conditions 5.4.2 Environmental factors as influx variables 5.4.3 Environmental factor complexes 6 Plant succession: processes and models 6.1 Biological processes of colonization and succession 6.1 Migration 6.2 Ecesis 6.3 Reaction 6.4 Facilitation 6.5 Competition 6.6 Allelopathy, herbivory and pathogens 6.7 Stabilization 6.2 Models 6.2.1 Monoclimax and polyclimax 6.2.2 Climax pattern and site climax 6.2.3 Relay floristics and IFC 6.2.4 Non-selective and selective autosuccession 6.2.5 Facilitation, tolerance and inhibition 6.2.6 Chronic disturbance, competitive hierarchy and resource ratio 6.2.7 Evolutionary strategies 6.2.8 Vital attributes, process interactions and a causal hierarchy 6.3 A geoecological model 6.3.1 Coupling of physical and biological processes 6.3.2 Spatio-temporal dynamics 7 The ecological significance of recently-deglaciated terrain 7.1 Chronosequences 7.2 The geoecological approach 7.3 Some broader implications References Index