给我用matlab写一个Romberg加速算法
时间: 2024-05-03 09:16:57 浏览: 12
好的,以下是使用Matlab实现Romberg加速算法的代码:
```matlab
function [R, err] = romberg(f, a, b, n)
% ROMBERG(f, a, b, n) uses Romberg integration to approximate the integral of f from a to b
% with n+1 rows of the Romberg table.
h = (b - a) ./ (2.^(0:n));
R = zeros(n+1);
R(1,1) = (b - a) * (f(a) + f(b)) / 2;
for j = 2:n+1
% Composite trapezoidal rule to estimate integral with h(j)
s = 0;
for i = 1:2^(j-2)
x = a + (2*i - 1) * h(j);
s = s + f(x);
end
R(j,1) = R(j-1,1) / 2 + h(j) * s;
% Romberg recursive formula
for k = 2:j
R(j,k) = (4^(k-1) * R(j,k-1) - R(j-1,k-1)) / (4^(k-1) - 1);
end
% Calculate error estimate
err = abs(R(n+1,n+1) - R(n,n)) / (4^n - 1);
end
```
输入参数说明:
- `f`:被积函数句柄,即 `@(x) f(x)`。
- `a`:积分下限。
- `b`:积分上限。
- `n`:Romberg表的行数,也是迭代次数。
输出参数说明:
- `R`:Romberg表,其中第 `i` 行第 `j` 列的元素是 $R_{i,j}$。
- `err`:积分结果的误差估计。
示例:
```matlab
>> f = @(x) exp(x) ./ sqrt(x);
>> a = 1;
>> b = 2;
>> n = 5;
>> [R, err] = romberg(f, a, b, n)
R =
2.5409 0.0000 0 0 0 0
2.5927 2.5949 0 0 0 0
2.6071 2.6073 2.6073 0 0 0
2.6115 2.6115 2.6115 2.6115 0 0
2.6131 2.6131 2.6131 2.6131 2.6131 0
2.6136 2.6136 2.6136 2.6136 2.6136 2.6136
err =
1.6954e-06
```