Numerical Integration.md

基本思想

计算 $I(f)\stackrel{\triangle}{=}\int_a^b f(x)dx$

• 思路1 ![[Pasted image 20240527202859.png]]
• 思路2 ![[Pasted image 20240527202920.png]] ![[Pasted image 20240527203009.png]]

插值型求积公式

![[Pasted image 20240527203459.png]]

积分余项

![[Pasted image 20240527203614.png]]

代数精度

![[Pasted image 20240527203714.png]] ![[Pasted image 20240527203826.png]]

求积公式的收敛性与稳定性

收敛性

![[Pasted image 20240527204359.png]]

敏感性

![[Pasted image 20240527204421.png]]

稳定性

![[Pasted image 20240527204551.png]] ![[Pasted image 20240527204559.png]]

[[Newton-Cotes formula]]

[[Composite Integration Rule]]

[[Richardson Extrapolation Method]]

[[Gaussian Quadrature Formula]]