G. Mathematics of Computing

• G.0 GENERAL
• G.1 NUMERICAL ANALYSIS
  • G.1.0 General
    • Computer arithmetic
    • Conditioning (and ill-conditioning) (revised 1998)
    • Error analysis
    • Interval arithmetic (new)
    • Multiple precision arithmetic (new)
    • Numerical algorithms
    • Parallel algorithms
    • Stability (and instability)
  • G.1.1 Interpolation (see also I.3.5, I.3.7)
    • Difference formulas (retired since 1998)
    • Extrapolation
    • Interpolation formulas
    • Smoothing
    • Spline and piecewise polynomial interpolation
  • G.1.2 Approximation
    • Approximation of surfaces and contours (new)
    • Chebyshev approximation and theory
    • Elementary function approximation
    • Fast Fourier transforms (FFT) (new)
    • Least squares approximation
    • Linear approximation
    • Minimax approximation and algorithms
    • Nonlinear approximation
    • Rational approximation
    • Special function approximations (new)
    • Spline and piecewise polynomial approximation
    • Wavelets and fractals (new)
  • G.1.3 Numerical Linear Algebra
    • Conditioning
    • Determinants (retired since 1998)
    • Eigenvalues and eigenvectors (direct and iterative methods) (revised 1998)
    • Error analysis
    • Linear systems (direct and iterative methods)
    • Matrix inversion
    • Pseudoinverses (retired since 1998)
    • Singular value decomposition (new)
    • Sparse, structured, and very large systems (direct and iterative methods) (revised 1998)
  • G.1.4 Quadrature and Numerical Differentiation (see also F.2.1)
    • Adaptive and iterative quadrature (revised 1998)
    • Automatic differentiation (new)
    • Equal interval integration (retired since 1998)
    • Error analysis
    • Finite difference methods
    • Gaussian quadrature
    • Iterative methods
    • Multidimensional (multiple) quadrature (revised 1998)
  • G.1.5 Roots of Nonlinear Equations
    • Continuation (homotopy) methods (new)
    • Convergence
    • Error analysis
    • Iterative methods
    • Polynomials, methods for
    • Systems of equations
  • G.1.6 Optimization
    • Constrained optimization
    • Convex programming (new)
    • Global optimization (new)
    • Gradient methods
    • Integer programming
    • Least squares methods
    • Linear programming
    • Nonlinear programming
    • Quadratic programming methods (new)
    • Simulated annealing (new)
    • Stochastic programming (new)
    • Unconstrained optimization (new)
  • G.1.7 Ordinary Differential Equations
    • Boundary value problems
    • Chaotic systems (new)
    • Convergence and stability
    • Differential-algebraic equations (new)
    • Error analysis
    • Finite difference methods (new)
    • Initial value problems
    • Multistep and multivalue methods (revised 1998)
    • One-step (single step) methods (revised 1998)
    • Stiff equations
  • G.1.8 Partial Differential Equations
    • Domain decomposition methods (new)
    • Elliptic equations
    • Finite difference methods (revised 1998)
    • Finite element methods
    • Finite volume methods (new)
    • Hyperbolic equations
    • Inverse problems (new)
    • Iterative solution techniques (new)
    • Method of lines
    • Multigrid and multilevel methods (new)
    • Parabolic equations
    • Spectral methods (new)
  • G.1.9 Integral Equations
    • Delay equations (new)
    • Fredholm equations
    • Integro-differential equations
    • Volterra equations
  • G.1.10 Applications (new)
  • G.1.m Miscellaneous
• G.2 DISCRETE MATHEMATICS
  • G.2.0 General
  • G.2.1 Combinatorics (see also F.2.2)
    • Combinatorial algorithms
    • Counting problems
    • Generating functions
    • Permutations and combinations
    • Recurrences and difference equations
  • G.2.2 Graph Theory (see also F.2.2)
    • Graph algorithms
    • Graph labeling (new)
    • Hypergraphs (new)
    • Network problems
    • Path and circuit problems
    • Trees
  • G.2.3 Applications (new)
  • G.2.m Miscellaneous
• G.3 PROBABILITY AND STATISTICS
  • Contingency table analysis (new)
  • Correlation and regression analysis (new)
  • Distribution functions (new)
  • Experimental design (new)
  • Markov processes (new)
  • Multivariate statistics (new)
  • Nonparametric statistics (new)
  • Probabilistic algorithms (including Monte Carlo)
  • Queueing theory (new)
  • Random number generation
  • Reliability and life testing (new)
  • Renewal theory (new)
  • Robust regression (new)
  • Statistical computing
  • Statistical software
  • Stochastic processes (new)
  • Survival analysis (new)
  • Time series analysis (new)
• G.4 MATHEMATICAL SOFTWARE
  • Algorithm design and analysis (revised 1998)
  • Certification and testing
  • Documentation (new)
  • Efficiency
  • Parallel and vector implementations (new)
  • Portability (retired since 1998)
  • Reliability and robustness
  • User interfaces (new)
  • Verification (retired since 1998)
• G.m MISCELLANEOUS
  • Queueing theory (retired since 1998)