User:Dfletter/ACM Mapping to WP/Mathematics of computing

=G. Mathematics of Computing =

G.1.0 General

 * Computer arithmetic
 * Conditioning (and ill-conditioning)
 * Error analysis
 * Interval arithmetic
 * Multiple precision arithmetic
 * Numerical algorithms
 * Parallel algorithms
 * Stability (and instability)

G.1.1 Interpolation (I.3.5, I.3.7)

 * Difference formulas [**]
 * Extrapolation
 * Interpolation formulas
 * Smoothing
 * Spline and piecewise polynomial interpolation

G.1.2 Approximation

 * Approximation of surfaces and contours
 * Chebyshev approximation and theory
 * Elementary function approximation
 * Fast Fourier transforms (FFT)
 * Least squares approximation
 * Linear approximation
 * Minimax approximation and algorithms
 * Nonlinear approximation
 * Rational approximation
 * Special function approximations
 * Spline and piecewise polynomial approximation
 * Wavelets and fractals

G.1.3 Numerical Linear Algebra

 * Conditioning
 * Determinants [**]
 * Eigenvalues and eigenvectors (direct and iterative methods)
 * Error analysis
 * Linear systems (direct and iterative methods)
 * Matrix inversion
 * Pseudoinverses [**]
 * Singular value decomposition
 * Sparse, structured, and very large systems (direct and iterative methods)

G.1.4 Quadrature and Numerical Differentiation (F.2.1)

 * Adaptive and iterative quadrature
 * Automatic differentiation
 * Equal interval integration [**]
 * Error analysis
 * Finite difference methods
 * Gaussian quadrature
 * Iterative methods
 * Multidimensional (multiple) quadrature

G.1.5 Roots of Nonlinear Equations

 * Continuation (homotopy) methods
 * Convergence
 * Error analysis
 * Iterative methods
 * Polynomials, methods for
 * Systems of equations

G.1.6 Optimization

 * Constrained optimization
 * Convex programming
 * Global optimization
 * Gradient methods
 * Integer programming
 * Least squares methods
 * Linear programming
 * Nonlinear programming
 * Quadratic programming methods
 * Simulated annealing
 * Stochastic programming
 * Unconstrained optimization

G.1.7 Ordinary Differential Equations

 * Boundary value problems
 * Chaotic systems
 * Convergence and stability
 * Differential-algebraic equations
 * Error analysis
 * Finite difference methods
 * Initial value problems
 * Multistep and multivalue methods
 * One-step (single step) methods
 * Stiff equations

G.1.8 Partial Differential Equations

 * Domain decomposition methods
 * Elliptic equations
 * Finite difference methods
 * Finite element methods
 * Finite volume methods
 * Hyperbolic equations
 * Inverse problems
 * Iterative solution techniques
 * Method of lines
 * Multigrid and multilevel methods
 * Parabolic equations
 * Spectral methods

G.1.9 Integral Equations

 * Delay equations
 * Fredholm equations
 * Integro-differential equations
 * Volterra equations

G.2.1 Combinatorics (F.2.2)

 * Combinatorial algorithms
 * Counting problems
 * Generating functions
 * Permutations and combinations
 * Recurrences and difference equations

G.2.2 Graph Theory (F.2.2)

 * Graph algorithms
 * Graph labeling
 * Hypergraphs
 * Network problems
 * Path and circuit problems
 * Trees

G.3 PROBABILITY AND STATISTICS

 * Contingency table analysis
 * Correlation and regression analysis
 * Distribution functions
 * Experimental design
 * Markov processes
 * Multivariate statistics
 * Nonparametric statistics
 * Probabilistic algorithms (including Monte Carlo)
 * Queueing theory
 * Random number generation
 * Reliability and life testing
 * Renewal theory
 * Robust regression
 * Statistical computing
 * Statistical software
 * Stochastic processes
 * Survival analysis
 * Time series analysis

G.4 MATHEMATICAL SOFTWARE

 * Algorithm design and analysis
 * Certification and testing
 * Documentation
 * Efficiency
 * Parallel and vector implementations
 * Portability [**]
 * Reliability and robustness
 * User interfaces
 * Verification [**]

G.m MISCELLANEOUS

 * Queueing theory [**]