## Misc.

• complex number
• scientific notatoin
• arbitrary precision support
• interval arithmetics
• a Math table data structure to store table values
• Ordinary Least Square solver
• sequence
• Fibonacci sequence
• uniroot finding algorithm:
• Brent
• Halley
• Newton
• common physical constants

## Linear Algebra

• vector
• vector space
• various matrix representations:
• bi-diagonal
• diagonal
• tri-diagonal
• Givens
• Hilbert
• lower/upper triangular
• permutation
• sparse vector representations:
• sparse matrix representations:
• CSR
• DOK
• LIL
• iterative sparse matrix solver:
• stationary
• Jacobi
• Gauss-Seidel
• SOR
• SSOR
• non-stationary
• Steepest Descent
• BiCG
• BiCGStabl
• CGNE
• CGNR
• CG
• CGS
• GCR
• GMRES
• MinRes
• QMR
• pre-conditioner support
• Jacobi
• SSOR
• customized
• matrix elementary operations
• Householder transformation
• matrix inverse
• matrix measures:
• determinant
• rank
• trace
• max
• min
• power of matrix
• matrix pseudoinverse
• matrix bi-diagonalization
• matrix tri-diagonalization
• Cholesky decomposition
• Doolittle factorization
• Eigen factorization
• Gauss-Jordan elimination
• SVD factorization (for asymmetric matrix)
• Gram-Schmidt factorization
• Hessenberg factorization
• LDL decomposition
• LU decomposition
• QR decomposition

## Curve Fitting & Interpolation

• curve fitting
• least-squares
• online interpolation
• the Neville method
• univariate
• linear
• Newton polynomial
• (natural) cubic spline
• cubic Hermite spline
• bivariate grid
• bilinear
• bicubic
• bicubic spline
• multivariate grid
• multi-linear
• multi-cubic spline
• general recursive grid interpolation

## Geometry

• comprehensive collection of trigonometric functions (complementary to Java’s Math class)
• point and line segment
• polygonal chain
• Ramer-Douglas-Peucker algorithm

## Functions

• polynomial
• polynomial evaluation using Horner scheme
• polynomial root finding using analytical formulae up to degree 4
• polynomial root finding using the Jenkins Traub method
• continued fraction
• special functions:
• Beta
• regularized Beta
• inverse of regularized Beta
• cumulative Normal
• inverse of cumulative Normal
• Digamma
• Erf
• inverse of Erf
• Gamma
• lower incomplete Gamma
• regularized Gamma P
• inverse of regularized Gamma P
• regularized Gamma Q
• incomplete upper Gamma
• Gaussian
• logBeta
• logGamma
• Lanczos method

## Calculus

• finite difference
• differentiation using Ridders’ method
• derivaties of functions for:
• Beta
• Beta Regularized
• Erf
• Gamma
• Gaussian
• multivariate differentiation:
• (bordered) Hessian
• Jacobian
• Riemann integration
• Riemann integration using substitution rules:
• Double-Exponential rule
• Exponential rule
• Power law singularity
• Map to the Standard interval
• integration using Romberg’s method
• integration using Newton-Cotes formula
• Simpson’s rule
• Trapezoidal rule
• Midpoint rule