11 articles
Adaptive quadrature
Adaptive quadrature is a numerical integration method that computes a definite integral to a requested accuracy by recursively subdividing the domain where the integrand varies most.
Bernstein polynomial
A Bernstein polynomial is a polynomial expressed as a combination of Bernstein basis functions on the unit interval, numerically stable and standard in computer-aided geometric design as the Bézier form.
Chebyshev approximation
Chebyshev approximation, also called minimax or uniform approximation, finds the polynomial minimizing a function's maximum error on an interval; it is computed by the Remez algorithm.
Convolution quadrature
Convolution quadrature is a numerical method, introduced by C. Lubich in 1988, that approximates convolution integrals on a uniform time grid using only the kernel's Laplace transform.
Hermite interpolation
Hermite interpolation is a polynomial interpolation method matching function values and derivatives at nodes; matching values and first derivatives at n nodes gives a unique polynomial of degree at most 2n − 1.
Newton interpolation
Newton interpolation is a numerical analysis method, attributed to Isaac Newton, for constructing the polynomial that passes through given data points, with coefficients given by the data's divided differences.
Padé approximant
A Padé approximant is a rational function whose power series expansion matches a given function's series to the highest possible order, often beating truncated Taylor series near poles.
Quadratic interpolation
Quadratic interpolation is a numerical analysis method that estimates intermediate function values by fitting the unique parabola through three known data points and evaluating it between them.
Quadrature rule
A quadrature rule is a numerical method that approximates a definite integral of a function by a weighted sum of its values at selected points, or nodes.
Rational interpolation
Rational interpolation approximates a function by a ratio of two polynomials forced through given data points, preferred over a single polynomial when the function has poles or nearly singular behavior.
Sparse grid
A sparse grid is a numerical construction that represents high-dimensional functions on a subset of a full tensor-product grid, using the Smolyak algorithm, enabling quadrature, interpolation, and surrogate modeling in tens of dimensions.