Question

the gaussian quadrature by using n+1 points is exact for polynomials of degree k satisfying what?

Answer 1

the gaussian quadrature by using n+1 points is exact for polynomials of degree k satisfying is K= 2n+ 1

Answer 2

Given : The Gaussian quadrature by  using n + 1 points is exact for

polynomials of degree k

To Find : k

Solution:

Gaussian quadrature rule named after Carl Friedrich Gauss,

An n-point Gaussian quadrature rule   is a quadrature rule   constructed to yield an exact result for polynomials of degree 2n − 1 or less

Here given points are n + 1

substitute  n + 1 in place of n  

polynomials of degree k = 2(n + 1) - 1

= 2n + 2 - 1

= 2n + 1

polynomials of degree k  satisfying  2n + 1

k = 2n + 1

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the gaussian quadrature by using n+1 points is exact for polynomials of degree k satisfying is K= 2n+ 1

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