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ⓘ Numerical integration is the term used for a number of methods to find an approximation for an integral. Numerical integration has also been called quadrature. ..




Numerical integration
                                     

ⓘ Numerical integration

Numerical integration is the term used for a number of methods to find an approximation for an integral. Numerical integration has also been called quadrature. Very often, it is not possible to solve integration analytically, for example when the data consists of a number of distinct measurements, or when the antiderivative is not known, and it is difficult, impractical or impossible to find it. In such cases, the integral can be written as a mathematical function defined over the interval in question, plus a function giving the error.

One way to find a numerical integral is using interpolation. Very often these interpolating functions are polynomials.

Various formulas have been studied for many years and become famous. For example, there is the Gaussian quadrature named after Gauss, the Newton-Cotes formula named after Isaac Newton, and the Euler-Maclaurin formula named after Leonhard Euler.

                                     

1. Numerical errors

Numerical errors can occur in any kind of numerical computation including numerical integration. Errors in numerical integration are considered in another area called "validated numerics".

                                     
  • invention of the double exponential integration formula one of the most effective method for numerical integration He also had several joint studies
  • numerical analysis and former professor at the University of Tokyo. He is known for his studies about numerical linear algebra, numerical integration
  • Validated Numerics abbreviated as SCAN is an international conference about numerical analysis such as numerical integration numerical linear algebra
  • validated numerics Numerical digit Numerical integration Numerical linear algebra Numerical methods for ordinary differential equations Numerical methods
  • Newton s method Numerical digit Numerical integration Numerical linear algebra Numerical methods for ordinary differential equations Numerical methods for
  • Romberg integration a famous numerical integration method is also based on this technique. Brezinski, C. 2019 Reminiscences of Peter Wynn, Numerical Algorithms
  • exponential integrators SIAM Journal on Scientific Computing, 33 2 488 - 511. Hairer, E., Lubich, C., & Wanner, G. 2006 Geometric numerical integration structure - preserving
  • A projection method for generalized eigenvalue problems using numerical integration en: Journal of computational and applied mathematics, 159 1 119 - 128
  • Numerical methods for partial differential equations are computational schemes to obtain approximate solutions of partial differential equations PDEs
  • Infinity Linear algebra Number theory Numerical analysis Numerical integration Numerical linear algebra Validated numerics Order of Operations Probability Statistics