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Words: 3k
Articles: 119
Numerical analysis studies algorithms for approximating mathematical problems and controlling their errors.
Table of contents
3k
119
Arithmetic operation
Numerical analysis
23
Schur stability criterion
Numerical analysis
32
Lie-Trotter splitting commutator error
Numerical analysis
22
Composite midpoint rule error
Numerical analysis
49
1
Quadratic substitution for a square-root endpoint singularity
Composite midpoint rule error
28
Polynomial interpolation
Numerical analysis
74
3
Lagrange interpolation polynomial
Polynomial interpolation
10
Divided difference
Polynomial interpolation
43
1
Newton interpolation polynomial
Divided difference
19
Discrete Fourier transform
Numerical analysis
144
6
Cooley--Tukey fast Fourier transform
Discrete Fourier transform
48
1
Even--odd fast Fourier transform recursion
Cooley--Tukey fast Fourier transform
17
Discrete cosine transform
Discrete Fourier transform
48
1
Discrete cosine transform from an even-reflected discrete Fourier transform
Discrete cosine transform
39
Discrete sine transform
Discrete Fourier transform
37
1
Discrete sine transform from a sign-modulated discrete cosine transform
Discrete sine transform
29
Gershgorin circle theorem
Numerical analysis
65
1
Gershgorin stability bound for a variable-coefficient diffusion stencil
Gershgorin circle theorem
50
Finite difference method
Numerical analysis
423
17
Central finite difference
Finite difference method
11
Forward difference operator
Finite difference method
54
2
Discrete antiderivative
Forward difference operator
17
Newton series for an integer-valued polynomial sequence
Forward difference operator
23
Von Neumann stability analysis
Finite difference method
145
5
Amplification factor
Von Neumann stability analysis
46
1
Amplification factor of a two-sided one-step stencil
Amplification factor
18
Amplification polynomial of a multilevel finite difference scheme
Von Neumann stability analysis
23
Crank-Nicolson diffusion scheme
Von Neumann stability analysis
22
Centered three-level wave scheme
Von Neumann stability analysis
20
Courant number
Finite difference method
24
Dirichlet discrete Laplacian
Finite difference method
173
5
Crank-Nicolson stability on a finite Dirichlet interval
Dirichlet discrete Laplacian
28
Five-point Dirichlet Laplacian as a Kronecker sum
Dirichlet discrete Laplacian
125
3
One-implicit-direction diffusion splitting
Five-point Dirichlet Laplacian as a Kronecker sum
87
2
Stability limit of one-implicit-direction diffusion splitting
One-implicit-direction diffusion splitting
37
Unconditionally stable corrected directional diffusion splitting
One-implicit-direction diffusion splitting
26
Thomas algorithm
Numerical analysis
22
Gaussian quadrature
Numerical analysis
19
Chebyshev polynomial
Numerical analysis
173
7
Chebyshev polynomial of the second kind
Chebyshev polynomial
28
Rational cosine of an integral submultiple of pi
Chebyshev polynomial
26
Positivity of Chebyshev derivatives beyond the unit interval
Chebyshev polynomial
22
Monic Chebyshev extremal polynomial
Chebyshev polynomial
22
Chebyshev polynomial domination lemma
Chebyshev polynomial
23
Chebyshev differential equation
Chebyshev polynomial
38
1
Chebyshev derivative Sturm-Liouville pair
Chebyshev differential equation
24
Backward differentiation formula
Numerical analysis
Constrained optimization
Numerical analysis
Equally spaced interpolation
Numerical analysis
Ford-Fulkerson algorithm
Numerical analysis
Givens rotation
Numerical analysis
51
1
QR decomposition by Givens rotations
Givens rotation
28
Gradient descent
Numerical analysis
216
9
Lipschitz gradient
Gradient descent
12
Exact line search for a positive-definite quadratic
Gradient descent
25
Conjugate gradient method
Gradient descent
75
2
Krylov subspace
Conjugate gradient method
13
Finite termination of the conjugate gradient method
Conjugate gradient method
32
Heavy-ball method
Gradient descent
86
3
Heavy-ball residual recurrence
Heavy-ball method
26
Heavy-ball error propagation matrix
Heavy-ball method
50
1
Heavy-ball rate for a two-eigenvalue diagonal quadratic
Heavy-ball error propagation matrix
21
Peano kernel theorem
Numerical analysis
56
2
Four-point one-sided second-derivative formula
Peano kernel theorem
36
1
Sharp Peano-kernel constant for the four-point endpoint second derivative
Four-point one-sided second-derivative formula
27
Periodic trapezoidal Fourier aliasing
Numerical analysis
36
Fourier-Galerkin matrix for a drift-diffusion equation
Numerical analysis
51
Fourier spectral method for variable-coefficient advection
Numerical analysis
98
3
Positive Fourier-symbol Toeplitz matrix
Fourier spectral method for variable-coefficient advection
25
Real spectrum of a positive-Hermitian times Hermitian product
Fourier spectral method for variable-coefficient advection
26
Explicit Euler instability on a nonzero imaginary eigenvalue
Fourier spectral method for variable-coefficient advection
25
Runge-Kutta method
Numerical analysis
84
4
Local truncation error
Runge-Kutta method
37
Implicit Runge-Kutta method
Runge-Kutta method
31
1
Trapezoidal rule
Implicit Runge-Kutta method
16
Order of a Runge-Kutta method
Runge-Kutta method
16
Simplex algorithm
Numerical analysis
Sparse optimization
Numerical analysis
Stability function
Numerical analysis
Multistep method
Numerical analysis
61
3
Zero-stability
Multistep method
35
1
Root condition for a multistep method
Zero-stability
15
Dahlquist equivalence theorem
Multistep method
12
Numerical linear algebra
Numerical analysis
484
18
Gaussian elimination
Numerical linear algebra
20
LDL decomposition
Numerical linear algebra
42
Machine precision
Numerical linear algebra
12
Eigenpair residual
Numerical linear algebra
39
1
Backward error of an approximate eigenpair
Eigenpair residual
26
Householder QR decomposition
Numerical linear algebra
19
Householder tridiagonalization
Numerical linear algebra
12
Unshifted QR algorithm
Numerical linear algebra
219
5
Accumulated QR factorization identity
Unshifted QR algorithm
53
Symmetric bandwidth preservation under QR iteration
Unshifted QR algorithm
33
Simultaneous iteration interpretation of the QR algorithm
Unshifted QR algorithm
87
1
Two-column dominant-subspace condition
Simultaneous iteration interpretation of the QR algorithm
60
Block deflation in the QR algorithm
Unshifted QR algorithm
26
Stationary iterative method for a linear system
Numerical linear algebra
111
4
Matrix splitting
Stationary iterative method for a linear system
40
1
Householder-John theorem
Matrix splitting
32
Jacobi method
Stationary iterative method for a linear system
45
1
Jacobi convergence for a symmetric positive-definite tridiagonal matrix
Jacobi method
28
Linear stability domain
Numerical analysis
186
5
Explicit Euler method
Linear stability domain
12
A-stability
Linear stability domain
51
1
A-stability of a symmetric two-stage implicit Runge-Kutta family
A-stability
38
Stiff two-mode linear system
Linear stability domain
47
Milne device for forward and backward Euler
Linear stability domain
43
Orthogonal polynomial
Numerical analysis
69
4
Monic orthogonal polynomial
Orthogonal polynomial
23
Hermite polynomial
Orthogonal polynomial
Zeros of orthogonal polynomials
Orthogonal polynomial
17
Jacobi matrix
Orthogonal polynomial
16
Quadrature rule
Numerical analysis
179
5
Nodal-polynomial criterion for quadrature exactness
Quadrature rule
30
Degree ceiling for quadrature exactness
Quadrature rule
32
Positivity of quadrature weights from degree 2n exactness
Quadrature rule
39
Convergence of positive quadrature rules
Quadrature rule
41
Moment matching
Quadrature rule
22
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Analysis
Area of mathematics
Mathematics
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