G. Mathematics of computing

G. Mathematics of computing : hovedinndeling

• G.0 - Mathematics of computing - General
• G.1 - Numerical analysis
• G.2 - Discrete mathematics
• G.3 - Probability and statistics
• G.4 - Mathematical software
• G.5 - Mathematical physics
• G.m - Mathematics of computing - Miscellaneous

G.0 - Mathematics of computing - General

G.1 - Numerical analysis

G.1.0 - Numerical analysis - General

Computer arithmetic; Condtioning (and ill-conditioning); Error analysis; Numerical algortihms; Parallel algorithms; Stability (and instability); Interval arithmetic; Multiple precision arithmetic;

G.1.1 - Interpolation

Difference formulas; Extrapolation; Interpolation formulas; Smoothing; Spline and piecewise polynomial interpolation;

G.1.2 - Approximation

Chebyshev approximation and theory; Elementary function approximation; Least square approximation; Linear approximation; Minimax approximation and algortihms; Nonlinear approximation; Rational approximation; Spline and piecewise polynomial approximation; Approximation of surfaces and contours; Fast Fourier tranforms; Special function approximations; 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; Sparse, structured and very large systems (direct and itrative methods); Singular value decomposition;

G.1.4 - Quadrature and numerical differentiation

Adaptive and iterative quadrature; Equal interval integration; Error analysis; Finite difference methods; Gaussian quadrature; Iterative methods; Multidimensional (multiple) quadrature; Automatic diffentiation;

G.1.5 - Roots of nonlinear equations

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

G.1.6 - Optimization

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

G.1.7 - Ordinary differential equations

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

G.1.8 - Partial differential equations

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

G.1.9 - Integral equations

G.1.10 - Applications

Fredholm equations; Integro-differential equations; Volterra equations; Delay equations;

G.1.m - Numerical analysis - Miscellaneous

G.2 - Discrete mathematics

G.2.0 - Discrete mathematics - General

G.2.1 - Combinatorics

Combinational algorithms; Counting problems; Generating functions; Permutations and combinations; Recurrences and difference equations;

G.2.2 - Graph theory

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

G.2.3 - Applications

G.2.m - Discrete mathematics - Miscellaneous

G.3, G.3.0 - Probability and statistics

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

G.4, G.4.0 - Mathematical software

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

G.5 - Mathematical physics

G.5.0 - Mathematical physics - general

G.5.1 - Dynamical systems - Chaos

G.5.2 - Fluid mechanics

G.m - Mathematics of computing - Miscellaneous

Queueing theory;