http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Ch. 1 Numerical Algorithms -- 1.1.Finding roots -- 1.2.Analyzing Heron's algorithm -- 1.3.Where to start -- 1.4.An unstable algorithm -- 1.5.General roots: effects of floating-point -- 1.6.Exercises -- 1.7.Solutions -- ch. 2 Nonlinear Equations -- 2.1.Fixed-point iteration -- 2.2.Particular methods -- 2.3.Complex roots -- 2.4.Error propagation -- 2.5.More reading -- 2.6.Exercises -- 2.7.Solutions -- ch. 3 Linear Systems -- 3.1.Gaussian elimination -- 3.2.Factorization -- 3.3.Triangular matrices -- 3.4.Pivoting -- 3.5.More reading -- 3.6.Exercises -- 3.7.Solutions -- ch. 4 Direct Solvers -- 4.1.Direct factorization -- 4.2.Caution about factorization -- 4.3.Banded matrices -- 4.4.More reading -- 4.5.Exercises -- 4.6.Solutions -- ch. 5 Vector Spaces -- 5.1.Normed vector spaces -- 5.2.Proving the triangle inequality -- 5.3.Relations between norms -- 5.4.Inner-product spaces -- 5.5.More reading -- 5.6.Exercises -- 5.7.Solutions -- ch. 6 Operators -- 6.1.Operators -- 6.2.Schur decomposition -- 6.3.Convergent matrices -- 6.4.Powers of matrices -- 6.5.Exercises -- 6.6.Solutions -- ch. 7 Nonlinear Systems -- 7.1.Functional iteration for systems -- 7.2.Newton's method -- 7.3.Limiting behavior of Newton's method -- 7.4.Mixing solvers -- 7.5.More reading -- 7.6.Exercises -- 7.7.Solutions -- ch. 8 Iterative Methods -- 8.1.Stationary iterative methods -- 8.2.General splittings -- 8.3.Necessary conditions for convergence -- 8.4.More reading -- 8.5.Exercises -- 8.6.Solutions -- ch. 9 Conjugate Gradients -- 9.1.Minimization methods -- 9.2.Conjugate Gradient iteration -- 9.3.Optimal approximation of CG -- 9.4.Comparing iterative solvers -- 9.5.More reading -- 9.6.Exercises -- 9.7.Solutions -- ch. 10 Polynomial Interpolation -- 10.1.Local approximation: Taylor's theorem -- 10.2.Distributed approximation: interpolation -- 10.3.Norms in infinite-dimensional spaces -- 10.4.More reading -- 10.5.Exercises -- 10.6.Solutions -- ch. 11 Chebyshev and Hermite Interpolation -- 11.1.Error term -- 11.2.Chebyshev basis functions -- 11.3.Lebesgue function -- 11.4.Generalized interpolation -- 11.5.More reading -- 11.6.Exercises -- 11.7.Solutions -- ch. 12 Approximation Theory -- 12.1.Best approximation by polynomials -- 12.2.Weierstrass and Bernstein -- 12.3.Least squares -- 12.4.Piecewise polynomial approximation -- 12.5.Adaptive approximation -- 12.6.More reading -- 12.7.Exercises -- 12.8.Solutions -- ch. 13 Numerical Quadrature -- 13.1.Interpolatory quadrature -- 13.2.Peano kernel theorem -- 13.3.Gregorie-Euler-Maclaurin formulas -- 13.4.Other quadrature rules -- 13.5.More reading -- 13.6.Exercises -- 13.7.Solutions -- ch. 14 Eigenvalue Problems -- 14.1.Eigenvalue examples -- 14.2.Gershgorin's theorem -- 14.3.Solving separately -- 14.4.How not to eigen -- 14.5.Reduction to Hessenberg form -- 14.6.More reading -- 11.7.Exercises -- 14.8.Solutions -- ch. 15 Eigenvalue Algorithms -- 15.1.Power method -- 15.2.Inverse iteration -- 15.3.Singular value decomposition -- 15.4.Comparing factorizations -- 15.5.More reading -- 15.6.Exercises -- 15.7.Solutions -- ch. 16 Ordinary Differential Equations -- 16.1.Basic theory of ODEs -- 16.2.Existence and uniqueness of solutions -- 16.3.Basic discretization methods -- 16.4.Convergence of discretization methods -- 16.5.More reading -- 16.6.Exercises -- 16.7.Solutions -- ch. 17 Higher-order ODE Discretization Methods -- 17.1.Higher-order discretization -- 17.2.Convergence conditions -- 17.3.Backward differentiation formulas -- 17.4.More reading -- 17.5.Exercises -- 17.6.Solutions -- ch. 18 Floating Point -- 18.1.Floating-point arithmetic -- 18.2.Errors in solving systems -- 18.3.More reading -- 18.4.Exercises -- 18.5.Solutions -- ch. 19 Notation.
Includes bibliographical references (pages [311]-322) and index.