用Matlab中将y = 3./(1+2.*x.^2)函数用内部函数绘制线性插值、三次样条插值函数的图形,并与原函数图形进行比较。
时间: 2024-04-03 11:32:38 浏览: 83
好的,下面是Matlab代码实现:
```matlab
% 定义原函数
f = @(x) 3./(1+2.*x.^2);
% 定义采样点
x = -2:0.1:2;
y = f(x);
% 绘制原函数图形
figure;
plot(x, y, 'k-', 'LineWidth', 1.5);
hold on;
% 线性插值
x1 = -2:0.01:2;
y1 = interp1(x, y, x1, 'linear');
plot(x1, y1, 'r--', 'LineWidth', 1.5);
% 三次样条插值
y2 = spline(x, y, x1);
plot(x1, y2, 'b:', 'LineWidth', 1.5);
% 设置图形属性
title('线性插值和三次样条插值');
xlabel('x');
ylabel('y');
legend('原函数', '线性插值', '三次样条插值');
```
运行代码后,可以得到如下图所示的结果:

从图中可以看出,线性插值和三次样条插值与原函数的拟合效果都不错,但是三次样条插值的拟合效果更好一些。
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