In this book the authors have assembled the best techniques from a great variety of sources, establishing a benchmark for the field of statistical computing. ---Mathematics of Computation . The text is highly readable and well illustrated with examples.  The reader who intends to take a hand in designing his own regression and multivariate packages will find a storehouse of information and a valuable resource in the field of statistical computing.

    1/ Introduction
    Presentation of Algorithms
    2/ Computer Organization
    2.1. Introduction
    2.2. Components of the Digital Computer System
    2.3 Representation of Numeric Values
    2.3.1 Integer Mode Representation
    2.3.2 Representation in Floating-Point Mode
    2.4 Floating- and Fixed- Point Arithmetic
    2.4.1 Floating-Point Arithmetic Operations
    2.4.2 Fixed-Point Arithmetic Operations
    3/ Error In Floating-Point Computation
    3.1 Introduction
    3.2 Types of Error
    3.3 Error Due to Approximation Imposed by the Computer
    3.4 Analyzing Error in a Finite Process
    3.5 Rounding Error in Floating-Point Computations
    3.6 Rounding Error in Two Common Floating-Point Calculations
    3.7 Condition and Numerical Stability
    3.8 Other Methods of Assessing Error in computation
    3.9 Summary
    4/ Programming and Statistical Software
    4.1 Programming Languages: Introduction
    4.2 Components of Programming Languages
    4.2.1 Data Types
    4.2.2 Data Structures
    4.2.3 Syntax
    4.2.4 Control Structures
    4.3 Program Development
    4.4 Statistical Software
    References and Further Readings
    5/ Approximating Probabilities and Percentage Selected Probability Distributions
    5.1 Notation and General Considerations
    5.1.1 Probability Distributions
    5.1.2 Accuracy Considerations
    5.2 General Methods in Approximation
    5.2.1 Approximate Transformation of Random Variables
    5.2.2 Closed Form Approximations
    5.2.3 General Series Expansion
    5.2.4 Exact Relationship Between Distributions
    5.2.5 Numerical Root Finding
    5.2.6 Continued Fractions
    5.2.7 Gaussian Quadrature
    5.2.8 Newton-Cotes Quadrature
    5.3 The Normal Distribution
    5.3.1 Normal Probabilities
    5.3.2 Normal Percentage Points
    5.4 Student’s t Distribution
    5.4.1 t Probabilities
    5.4.2 t-Percentage Points
    5.5 The Beta Distributions
    5.5.1 Evaluating the Incomplete Beta Function
    5.5.2 Inverting the Incomplete Beta Function
    5.6 F Distribution
    5.6.1 F Probabilities
    5.6.2 F Percentage Points
    5.7 Chi-Square Distribution
    5.7.1 Chi-Square Probabilities
    5.7.2 Chi-Square Percentage Points
    References and Further Readings
    6/ Random Numbers: Generation, Tests and Applications
    6.1 Introduction
    6.2 Generation of Uniform Random Numbers
    6.2.1 Congruential Methods
    6.2.2 Feedback Shift Register Methods
    6.2.3 Coupled Generators
    6.2.4 Portable Generators
    6.3 Tests of Random Number Generators
    6.3.1 Theoretical Tests
    6.3.2 Empirical Tests
    6.3.3 Selecting a Random Number Generator
    6.4 General Techniques for Generation of Nonuniform Random Deviates
    6.4.1 Use of the Cumulative Distribution Function
    6.4.2 Use of Mixtures of Distributions
    6.4.3 Rejection Methods
    6.4.4 Table Sampling Methods for Discrete Distributions
    6.4.5 The Alias Method for Discrete Distributions
    6.5 generation of Variates from Specific Distributions
    6.5.1 The Normal Distribution
    6.5.2 The Gamma Distribution
    6.5.3 The Beta Distribution
    6.5.4 The F, t, and Chi-Square Distributions
    6.5.5 The Binomial Distribution
    6.5.6 The Poisson Distribution
    6.5.7 Distribution of Order Statistics
    6.5.8 Some Other Univariate Distributions
    6.5.9 The Multivariate Normal Distribution
    6.5.10 Some Other Multivariate Distributions
    6.6 Applications
    6.6.1 The Monte Carlo Method
    6.6.2 Sampling and Randomization
    References and Further Readings
    7/ Selected Computational Methods In Linear Algebra
    7.1 Introduction
    7.2 Methods Bases on Orthogonal Transformations
    7.2.1 Householder Transformations
    7.2.2 Givens Transformations
    7.2.3 The Modified Gram-Schmidt Method
    7.2.4 Singular-value Decomposition
    7.3 Gaussian Elimination and the Sweep Operator
    7.4 Cholesky Decomposition and Rank-One Update
    References and Further Readings
    8/ Computational Methods for Multiple Linear Regression Analysis
    8.1 Basic Computational Methods
    8.1.1 Methods Using Orthogonal Triangularization of X
    8.1.2 Sweep Operations and Normal Equations
    8.1.3 Checking Programs, Computed Results and Improving Solutions Iteratively
    8.2 Regression Model Building
    8.2.1 All Possible Regressions
    8.2.2 Stepwise Regression
    8.2.3 Other Methods
    8.2.4 A Special Case—Polynomial Models
    8.3 Multiple Regression Under Linear Restrictions
    8.3.1 Linear Equality Restrictions
    8.3.2 Linear Inequality Restrictions
    References and Further Readings
    9/ Computational Methods For Classification Models
    9.1 Introduction
    9.1.1 Fixed-effects Models
    9.1.2 Restrictions on Models and Constraints on Solutions
    9.1.3 Reductions in Sums of squares
    9.1.4 An Example
    9.2 The Special Case of Balance and Completeness for Fixed-Effects Models
    9.2.1 Basic definitions and considerations
    9.2.2 Computer-related Considerations in the Special Case
    9.2.3 Analysis of Covariance
    9.3 The General Problem for Fixed-Effects Models
    9.3.1 Estimable Functions
    9.3.2 Selection Criterion 1
    9.3.3 Selection Criterion 2
    9.3.4 Summary
    9.4 Computing Expected Mean Squares and Estimates of Variance Components
    9.4.1 Computing Expected Mean Squares
    9.4.2 Variance Component Estimation
    References and Further Readings
    10/ Unconstrained Optimization and Nonlinear Regression
    10.1 Preliminaries
    10.1.1 Iteration
    10.1.2 Function Minima
    10.1.3 Step Direction
    10.1.4 Step Size
    10.1.5 Convergence of the Iterative Methods
    10.1.6 Termination of Iteration
    10.2 Methods for Unconstrained Minimization
    10.2.1 Method of Steepest Descent
    10.2.2 Newton’s Method and Some Modifications
    10.2.3 Quasi-Newton Methods
    10.2.4 Conjugate Gradient Method
    10.2.5 Conjugate Direction Method
    10.2.6 Other Derivative-Free Methods
    10.3 Computational Methods in Nonlinear Regression
    10.3.1 Newton’s Method for the Nonlinear Regression Problem
    10.3.2 The Modified Gauss-Newton Method
    10.3.3 The Levenberg-Marquardt Modification of Gauss-Newton
    10.3.4 Alternative Gradient Methods
    10.3.5 Minimization Without Derivatives
    10.3.6 Summary
    10.4 Test Problems
    References and Further Readings
    11/ Model Fitting Based on Criteria Other Than Least Squares
    11.1 Introduction
    11.2 Minimum L Norm Estimators
    11.2.1 Lᵖ Estimation
    11.2.2 L I͚ Estimators
    11.4 Biased Estimation
    11.5 Robust Nonlinear Regression
    References and Further Readings
    12/ Selected Multivariate Methods
    12.1 Introduction
    12.2 Canonical Correlations
    12.3 Principal Components
    12.4 Factor Analysis
    12.5 Multivariate Analysis of Variance
    References and Further Readings


    Martorell, Sebastián; Guedes Soares, Carlos; Barnett, Julie

    "The publication of this book, I believe, is a milestone. . .Kennedy and Gentle have done an outstanding job of assembling the best techniques from a great variety of sources, establishing a benchmark for the field of statistical computing. "
    ---Mathematics of Computation
    ". . .a very impressive text. . .highly readable and well illustrated with examples. . . .the reader who intends to take a hand in designing his own regression and multivariate packages will find a storehouse of information. "
    ---Journal of the American Statistical Association
    ". . .a valuable addition to the literature on statistical computing. "
    ---Mathematical Reviews