65-XX
|
Numerical analysis
|
65-00
|
General reference works (handbooks, dictionaries, bibliographies, etc.)
|
65-01
|
Instructional exposition (textbooks, tutorial papers, etc.)
|
65-02
|
Research exposition (monographs, survey articles)
|
65-03
|
Historical {!must also be assigned at least one classification number from section 01}
|
65-04
|
Explicit machine computation and programs (not the theory of computation or programming)
|
65-05
|
Experimental papers
|
65-06
|
Proceedings, conferences, collections, etc.
|
65A05
|
Tables
|
65Bxx
|
Acceleration of convergence
|
65B05
|
Extrapolation to the limit, deferred corrections
|
65B10
|
Summation of series
|
65B15
|
Euler - Maclaurin formula
|
65B99
|
None of the above, but in this section
|
65Cxx
|
Probabilistic methods, simulation and stochastic differential equations
{For theoretical aspects, see
68U20
and
60H35}
|
65C05
|
Monte_Carlo methods
|
65C10
|
Random number generation
|
65C20
|
Models, numerical methods
[See also
68U20]
|
65C30
|
Stochastic differential and integral equations
|
65C35
|
Stochastic particle methods
[See also
82C80]
|
65C40
|
Computational Markov chains
|
65C50
|
Other computational problems in probability
|
65C60
|
Computational problems in statistics
|
65C99
|
None of the above, but in this section
|
65Dxx
|
Numerical approximation and computational geometry (primarily algorithms)
{For theory, see
41-XX
and
68Uxx}
|
65D05
|
Interpolation
|
65D07
|
Splines
|
65D10
|
Smoothing, curve fitting
|
65D15
|
Algorithms for functional approximation
|
65D17
|
Computer aided design (modeling of curves and surfaces)
[See also
68U07]
|
65D18
|
Computer graphics and computational geometry
[See also
51N05,
68U05]
|
65D20
|
Computation of special functions, construction of tables
[See also
33F05]
|
65D25
|
Numerical differentiation
|
65D30
|
Numerical integration
|
65D32
|
Quadrature and cubature formulas
|
65D99
|
None of the above, but in this section
|
65E05
|
Numerical methods in complex analysis (potential theory, etc.)
{For numerical methods in conformal mapping, see
30C30}
|
65Fxx
|
Numerical linear algebra
|
65F05
|
Direct methods for linear systems and matrix inversion
|
65F10
|
Iterative methods for linear systems
[See also
65N22]
|
65F15
|
Eigenvalues, eigenvectors
|
65F18
|
Inverse eigenvalue problems
|
65F20
|
Overdetermined systems, pseudoinverses
|
65F22
|
Ill-posedness, regularization
|
65F25
|
Orthogonalization
|
65F30
|
Other matrix algorithms
|
65F35
|
Matrix norms, conditioning, scaling
[See also
15A12,
15A60]
|
65F40
|
Determinants
|
65F50
|
Sparse matrices
|
65F99
|
None of the above, but in this section
|
65Gxx
|
Error analysis and interval analysis
|
65G20
|
Algorithm with automatic result verification
|
65G30
|
Interval and finite arithmetic
|
65G40
|
General methods in interval analysis
|
65G50
|
Roundoff error
|
65G99
|
None of the above, but in this section
|
65Hxx
|
Nonlinear algebraic or transcendental equations
|
65H05
|
Single equations
|
65H10
|
Systems of equations
|
65H17
|
Eigenvalues, eigenvectors
[See also
58C40,
58E07,
47Hxx,
47Jxx,
90C30]
|
65H20
|
Global methods, including homotopy approaches
[See also
58C30,
90C30]
|
65H99
|
None of the above, but in this section
|
65Jxx
|
Numerical analysis in abstract spaces
|
65J05
|
General theory
|
65J10
|
Equations with linear operators {!do not use
65Fxx}
|
65J15
|
Equations with nonlinear operators {!do not use
65Hxx}
|
65J20
|
Improperly posed problems; regularization
|
65J22
|
Inverse problems
|
65J99
|
None of the above, but in this section
|
65Kxx
|
Mathematical programming, optimization and variational techniques
|
65K05
|
Mathematical programming (algorithms)
{For theory, see
90Cxx}
|
65K10
|
Optimization and variational techniques
[See also
49Mxx,
93B40]
|
65K99
|
None of the above, but in this section
|
65Lxx
|
Ordinary differential equations
|
65L05
|
Initial value problems
|
65L06
|
Multistep, Runge - Kutta and extrapolation methods
|
65L07
|
Numerical investigation of stability of solutions
|
65L08
|
Improperly posed problems
|
65L09
|
Inverse problems
|
65L10
|
Boundary value problems
|
65L12
|
Finite difference methods
|
65L15
|
Eigenvalue problems
|
65L20
|
Stability and convergence of numerical methods
|
65L50
|
Mesh generation and refinement
|
65L60
|
Finite elements, Rayleigh - Ritz, Galerkin and collocation methods
|
65L70
|
Error bounds
|
65L80
|
Methods for differential-algebraic equations
|
65L99
|
None of the above, but in this section
|
65Mxx
|
Partial differential equations, initial value and time-dependent initial-boundary value problems
|
65M06
|
Finite difference methods
|
65M12
|
Stability and convergence of numerical methods
|
65M15
|
Error bounds
|
65M20
|
Method of lines
|
65M25
|
Method of characteristics
|
65M30
|
Improperly posed problems
|
65M32
|
Inverse problems
|
65M50
|
Mesh generation and refinement
|
65M55
|
Multigrid methods; domain decomposition
|
65M60
|
Finite elements, Rayleigh - Ritz and Galerkin methods, finite methods
|
65M70
|
Spectral, collocation and related methods
|
65M99
|
None of the above, but in this section
|
65Nxx
|
Partial differential equations, boundary value problems
|
65N06
|
Finite difference methods
|
65N12
|
Stability and convergence of numerical methods
|
65N15
|
Error bounds
|
65N21
|
Inverse problems
|
65N22
|
Solution of discretized equations
[See also
65Fxx,
65Hxx]
|
65N25
|
Eigenvalue problems
|
65N30
|
Finite elements, Rayleigh - Ritz and Galerkin methods, finite methods
|
65N35
|
Spectral, collocation and related methods
|
65N38
|
Boundary element methods
|
65N40
|
Method of lines
|
65N45
|
Method of contraction of the boundary
|
65N50
|
Mesh generation and refinement
|
65N55
|
Multigrid methods; domain decomposition
|
65N99
|
None of the above, but in this section
|
65Pxx
|
Numerical problems in dynamical systems
[See also
37Mxx]
|
65P10
|
Hamiltonian systems including symplectic integrators
|
65P20
|
Numerical chaos
|
65P30
|
Bifurcation problems
|
65P40
|
Nonlinear stabilities
|
65P99
|
None of the above, but in this section
|
65Q05
|
Difference and functional equations, recurrence relations
|
65Rxx
|
Integral equations, integral transforms
|
65R10
|
Integral transforms
|
65R20
|
Integral equations
|
65R30
|
Improperly posed problems
|
65R32
|
Inverse problems
|
65R99
|
None of the above but in this section
|
65S05
|
Graphical methods
|
65Txx
|
Numerical methods in Fourier analysis
|
65T40
|
Trigonometric approximation and interpolation
|
65T50
|
Discrete and fast Fourier transforms
|
65T60
|
Wavelets
|
65T99
|
None of the above, but in this section
|
65Yxx
|
Computer aspects of numerical algorithms
|
65Y05
|
Parallel computation
|
65Y10
|
Algorithms for specific classes of architectures
|
65Y15
|
Packaged methods
|
65Y20
|
Complexity and performance of numerical algorithms
[See also
68Q25]
|
65Y99
|
None of the above, but in this section
|
65Z05
|
Applications to physics
|