Question

What does it mean by the approximation $\int_a^bf(x)dx\approx\sum_{i=0}^nA_if(x_i)$ is exact for all polynomials of degree up to $2n+1$?

score 164 · Answer 1 · 2016-04-20 08:18:46

What does it mean by the approximation $\int_a^bf(x)dx\approx\sum_{i=0}^nA_if(x_i)$ is exact for all polynomials of degree up to $2n+1$?

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List Question

What does it mean by the approximation $\int_a^bf(x)dx\approx\sum_{i=0}^nA_if(x_i)$ is exact for all polynomials of degree up to $2n+1$?

Approximate roots of nonlinear equation (non-integer polynomial)

Approximation of a quotient that involves the Lambert function.

How to solve this question using approximation theory?

Numerical Analysis: Approximations -- Discrete Average Value Theorem

Can a discrete function converge to a continous function?

$N$ is approximately linear in $d$ for $N^d=\frac12 e^{N}$

Approximating the integral of a large product

A fast converging limit for $\ln x$ (or why $\ln 2 \approx \sqrt{\sqrt{42}-6})$

Approximate value of k

Approximation, Truncation argument, Sobolev space

Approximating Fresnel integrals with standard functions

For $f(x)=x^4$, find its projection $f(x)^*\in P^2(-1,1)$ onto $W$

Error bound for function limit with arbitrary $\Delta h$

Uniform approximation. Two boundary layers?

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