Gauss-Jacobi Mechanical Quadrature

Gauss-Jacobi Mechanical Quadrature

Let "x"1 < "x"2 < ... < "x"n are the zeros of polynomial "p"n("x")of degree "n". Then there exist real numbers λ1, λ2, ... λn such that

int_a^b f(x) omega(x) , dx = lambda_1 f(x_1) + lambda_2 f(x_2) + ... + lambda_n f(x_n)

for any function "f"("x") that is an arbitrary polynomial of degree 2"n" - 1. Function ω("x") (called the "weight function") is positive on interval ("a", "b"). Numbers λ1, λ2, ... λn are called Christoffel numbers. The weight function ω("x") and the integer "n" uniquely determine Christoffel numbers. [Weisstein, Eric W."Gauss-Jacobi Mechanical Quadrature" From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Gauss-JacobiMechanicalQuadrature.html]

References

* Weisstein, Eric W. "Gauss-Jacobi Mechanical Quadrature." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Gauss-JacobiMechanicalQuadrature.html


Wikimedia Foundation. 2010.

Игры ⚽ Поможем сделать НИР

Look at other dictionaries:

  • List of numerical analysis topics — This is a list of numerical analysis topics, by Wikipedia page. Contents 1 General 2 Error 3 Elementary and special functions 4 Numerical linear algebra …   Wikipedia

  • mathematics — /math euh mat iks/, n. 1. (used with a sing. v.) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. 2. (used with a sing. or pl. v.) mathematical procedures,… …   Universalium

  • Numerical analysis — Babylonian clay tablet BC 7289 (c. 1800–1600 BC) with annotations. The approximation of the square root of 2 is four sexagesimal figures, which is about six decimal figures. 1 + 24/60 + 51/602 + 10/603 = 1.41421296...[1] Numerical analysis is the …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”