逐次分半法求积分matlab的代码

下面是使用逐次分半法（二分法）求定积分的 MATLAB 代码：

function [I,err] = bisection_integrate(f,a,b,tol)
% Bisection method for definite integration
% f: function handle of a scalar variable
% a, b: integration interval
% tol: tolerance for error
% I: approximation of the definite integral
% err: error estimate

if nargin < 4
    tol = 1e-6; % default tolerance
end

fa = f(a);
fb = f(b);
I1 = (b-a)*(fa+fb)/2; % initial approximation
err = inf;

while err > tol
    c = (a+b)/2;
    fc = f(c);
    I2 = (b-c)*(fb+fc)/2 + (c-a)*(fc+fa)/2; % approximation with two subintervals
    err = abs(I2-I1)/3; % error estimate
    I1 = I2;
    if fc*fa >= 0
        a = c;
        fa = fc;
    else
        b = c;
        fb = fc;
    end
end

I = I2;
end

使用方法示例：

f = @(x) exp(-x.^2); % function to integrate
a = 0; b = 1; % integration interval
[I,err] = bisection_integrate(f,a,b,1e-6);
fprintf('Integral value: %.8f\n', I);
fprintf('Error estimate: %.8f\n', err);

其中，`f` 是要求积分的函数句柄，`a` 和 `b` 分别是积分区间的下限和上限，`tol` 是误差容限，可以不指定，默认值为 `1e-6`。函数返回值 `I` 是积分的近似值，`err` 是误差估计。