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Numerical analysis is the study of computation and its accuracy, stability and often its implementation on a computer. This book focuses on the principles of numerical analysis and is intended to equip those readers who use statistics to craft their own software and to understand the advantages and disadvantages of different numerical methods.

Numerical Analysis for Statisticians

Recurrence Relations.- Power Series Expansions.- Continued Fraction Expansions.- Asymptotic Expansions.- Solution of Nonlinear Equations.- Vector and Matrix Norms.- Linear Regression and Matrix Inversion.- Eigenvalues and Eigenvectors.- Singular Value Decomposition.- Splines.- Optimization Theory.- The MM Algorithm.- The EM Algorithm.- Newton's Method and Scoring.- Local and Global Convergence.- Advanced Optimization Topics.- Concrete Hilbert Spaces.- Quadrature Methods.- The Fourier Transform.- The Finite Fourier Transform.- Wavelets.- Generating Random Deviates.- Independent Monte Carlo.- Permutation Tests and the Bootstrap.- Finite-State Markov Chains.- Markov Chain Monte Carlo.- Advanced Topics in MCMC.