Contents
ALGORITHMS
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FAQ
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TERMS OF USE
Site map
News
About the site
FAQ
Terms of use
Differential equations
Euler's method
Runge-Kutta method
Runge-Kutta method for a system of ODEs
Bulirsch-Stoer method for a system of ODEs
Systems of linear equations
General matrices
General real matrix
General complex matrix
Symmetric matrices
Symmetric positive definite matrix
Symmetric indefinite matrix
Other
Matrix and vector operations
Operations on general matrices
LU decomposition of a rectangular matrix
QR decomposition of a rectangular matrix
LQ decomposition of a rectangular matrix
Singular value decomposition
Schur decomposition
Determinant
Matrix inverse
Update of the inverse matrix by the Sherman-Morrison formula
Estimate of the condition number
Reduction of a general matrix to bidiagonal form
Reduction of a square matrix to upper Hessenberg form
Operations on complex matrices
LU decomposition of a general complex matrix
Determinant of a complex matrix
Complex matrix inverse
Complex matrix condition number estimate
Operations on symmetric matrices
Cholesky decomposition
LDLT decomposition
Determinant of a symmetric positive definite matrix
Determinant of a symmetric indefinite matrix
Inverse of a symmetric positive definite matrix
Inverse of a symmetric indefinite matrix
Condition number estimate of a symmetric positive definite matrix
Condition number estimate of a symmetric indefinite matrix
Reduction of a symmetric matrix to tridiagonal form
Operations on Hermitian matrices
Cholesky decomposition
Reduction of a Hermitian matrix to real tridiagonal form by the orthogonal similarity transformation.
Operations on other matrices
Triangular matrix inverse
Bidiagonal singular value decomposition
Schur decomposition of a real upper Hessenberg matrix
Matrix 1-norm estimation
Complex triangular matrix inverse
Eigenvalues and eigenvectors
Symmetric eigenproblems
Symmetric eigenproblem
Symmetric eigenproblem: bisection and inverse iteration
Generalized symmetric positive definite eigenproblem
Symmetric tridiagonal eigenproblem
Real symmetric tridiagonal eigenproblem: bisection and inverse iteration
Hermitian eigenproblems
Hermitian eigenproblem
Hermitian eigenproblem: bisection and inverse iteration
Nonsymmetric eigenproblems
Nonsymmetric eigenproblem
Numerical integration
Gaussian quadratures
Computation of Gauss-Legendre quadrature rule nodes and weights
Computation of Gauss-Chebyshev quadrature rule nodes and weights
Computation of Gauss-Jacobi quadrature rule nodes and weights
Computation of Gauss-Hermite quadrature rule nodes and weights
Computation of Gauss-Laguerre quadrature rule nodes and weights
Computation of Gauss quadrature rule nodes and weights
Computation of Gauss-Radau quadrature rule nodes and weights
Computation of Gauss-Lobatto quadrature rule nodes and weights
Simpson's method
Adaptive integration using a 61-point Gauss-Kronrod quadrature
Interpolation and approximation
Polynomial interpolation
Rational interpolation
Spline interpolation
Linear least squares approximation
Bilinear and bicubic spline interpolation
Univariate and multivariate optimization
Brent's method
L-BFGS algorithm
L-BFGS-B algorithm
Levenberg-Marquardt algorithm
Statistics
Hypothesis testing
Student's t-tests
F-test and chi-square test
Sign test
Wilcoxon signed-rank test
Mann-Whitney U-test
Jarque-Bera test
Significance test for correlation coefficient
Descriptive statistics
Correlation
Special functions
Orthogonal polynomials
Chebyshev polynomials
Hermite polynomials
Laguerre polynomials
Legendre polynomials
Distributions
F-distribution
Chi-square distribution
Binomial distribution
Poisson distribution
Student's t-distribution
Normal distribution, error function
Gamma function
Incomplete gamma function
Psi function
Beta function
Incomplete beta function
Bessel functions of integer order
Bessel functions of fractional order
Elliptic integrals of the first and second kind
Jacobian elliptic functions
Hypergeometric function 2F1
Confluent hypergeometric function 1F1
Dawson integral
Exponential integrals
Ei(x)
and
En(x)
Trigonometric integrals
Fresnel integrals
C(x)
and
S(x)
Airy functions
Ai(x)
and
Bi(x)
Sergey Bochkanov, Vladimir Bystritsky
Copyright © 1999-2008
