Uses of Interface
dev.nm.analysis.integration.univariate.riemann.Integrator
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Uses of Integrator in dev.nm.analysis.integration.univariate.riemann
Subinterfaces of Integrator in dev.nm.analysis.integration.univariate.riemann Modifier and Type Interface Description interface
IterativeIntegrator
An iterative integrator computes an integral by a series of sums, which approximates the value of the integral.Classes in dev.nm.analysis.integration.univariate.riemann that implement Integrator Modifier and Type Class Description class
ChangeOfVariable
Change of variable can easy the computation of some integrals, such as improper integrals.class
Riemann
This is a wrapper class that integrates a function by using an appropriate integrator together with Romberg's method.Constructors in dev.nm.analysis.integration.univariate.riemann with parameters of type Integrator Constructor Description ChangeOfVariable(SubstitutionRule change, Integrator integrator)
Construct an integrator that uses change of variable to do integration. -
Uses of Integrator in dev.nm.analysis.integration.univariate.riemann.gaussian
Classes in dev.nm.analysis.integration.univariate.riemann.gaussian that implement Integrator Modifier and Type Class Description class
GaussChebyshevQuadrature
Gauss-Chebyshev Quadrature uses the following weighting function: \[ w(x) = \frac{1}{\sqrt{1 - x^2}} \] to evaluate integrals in the interval (-1, 1).class
GaussHermiteQuadrature
Gauss-Hermite quadrature exploits the fact that quadrature approximations are open integration formulas (that is, the values of the endpoints are not required) to evaluate of integrals in the range \((-\infty, \infty )\).class
GaussianQuadrature
A quadrature rule is a method of numerical integration in which we approximate the integral of a function by a weighted sum of sample points.class
GaussLaguerreQuadrature
Gauss-Laguerre quadrature exploits the fact that quadrature approximations are open integration formulas (i.e.class
GaussLegendreQuadrature
Gauss-Legendre quadrature considers the simplest case of uniform weighting: \(w(x) = 1\). -
Uses of Integrator in dev.nm.analysis.integration.univariate.riemann.newtoncotes
Classes in dev.nm.analysis.integration.univariate.riemann.newtoncotes that implement Integrator Modifier and Type Class Description class
Midpoint
The midpoint rule computes an approximation to a definite integral, made by finding the area of a collection of rectangles whose heights are determined by the values of the function.class
NewtonCotes
The Newton-Cotes formulae, also called the Newton-Cotes quadrature rules or simply Newton-Cotes rules, are a group of formulae for numerical integration (also called quadrature) based on evaluating the integrand at equally-spaced points.class
Romberg
Romberg's method computes an integral by generating a sequence of estimations of the integral value and then doing an extrapolation.class
Simpson
Simpson's rule can be thought of as a special case of Romberg's method.class
Trapezoidal
The Trapezoidal rule is a closed type Newton-Cotes formula, where the integral interval is evenly divided into N sub-intervals.
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