写一个matlab程序为三点两次插值法极小化

以下是一个简单的 Matlab 程序，使用三点两次插值法进行极小值搜索：

function [x_min, y_min] = three_point_interpolation(x1, x2, x3, y1, y2, y3)
% Three-point interpolation method for finding the minimum of a function
% defined by three points (x1, y1), (x2, y2), and (x3, y3)

% Compute the coefficients of the quadratic interpolation polynomial
a = (y3 - 2*y2 + y1) / ((x3 - x2)*(x1 - x2));
b = (y2 - y1) / (x2 - x1) - a*(x1 + x2);
c = y1 - a*x1^2 - b*x1;

% Compute the x-coordinate of the minimum of the quadratic polynomial
x_min = -b / (2*a);

% Compute the y-coordinate of the minimum of the quadratic polynomial
y_min = a*x_min^2 + b*x_min + c;

end

要使用此函数，只需提供三个点的 x 和 y 坐标，如下所示：

x1 = 0;
x2 = 1;
x3 = 2;
y1 = 1;
y2 = 0;
y3 = 4;

[x_min, y_min] = three_point_interpolation(x1, x2, x3, y1, y2, y3);

这将计算三个点 (0,1), (1,0), 和 (2,4) 形成的函数的极小值，并将其存储在变量 x_min 和 y_min 中。