Gaussian quadrature
where f,w are continuous functions and the weight function w(x) is positive. Then
defines an inner product on the space of continuous functions, and an orthonormal sequence pn(x) of polynomials may be constructed such that pn(x) has degree n. Gauss then showed that pn + 1(x) has n + 1 distinct real roots x0,…,xn in (a,b) and that there are unique solutions W0,…,Wn to the equations
It is then the case that
exactly equals I(f) for polynomials of degree 2n + 1 or less, and more generally for continuous functions Qn(f) tends to I(f) as n→∞.
- distance between two lines
- distance between two points
- distance between two points
- distance from a point to a line
- distance from a point to a plane
- distance‐time graph
- distinct
- distribution
- distribution
- distribution function
- distribution‐free methods
- distributive
- div
- diverge
- divergence
- divergence theorem
- divides
- divisible
- division
- division
- division algebra
- Division Algorithm
- division ring
- divisor
- divisor function