java要求 输入两个不同函数：如f(x)=x2-3和f(x)=√x，通过牛顿迭代公式，计算其平方根。怎么用代码实现

在Java中，我们可以创建一个抽象类或者接口`Function`，然后为每个函数（如`f1(x)`和`f2(x)`）实现这个接口。接下来，我们使用牛顿迭代法（也叫牛顿-拉弗森方法），它是一种数值方法，用于找到方程的近似解。以下是代码的一个简单示例：

import java.lang.Math;

interface Function {
    double apply(double x);
}

class SquareFunction implements Function {
    @Override
    public double apply(double x) {
        return x * x - 3;
    }
}

class RootFunction implements Function {
    private final Function functionToSquareRoot;

    public RootFunction(Function functionToSquareRoot) {
        this.functionToSquareRoot = functionToSquareRoot;
    }

    @Override
    public double apply(double x) {
        // 使用牛顿迭代法计算sqrt(f(x))
        double guess = x; // 初始猜测值
        while (Math.abs(apply(guess) - functionToSquareRoot.apply(guess)) > epsilon) { // 设置一个足够小的精度阈值epsilon
            guess = guess - (apply(guess) / functionToSquareRoot.apply(guess));
        }
        return guess;
    }
}

public class Main {
    public static void main(String[] args) {
        Function squareFunction = new SquareFunction();
        Function rootFunction = new RootFunction(squareFunction);

        double initialGuess = 10; // 首次迭代猜测
        double result = rootFunction.apply(initialGuess);
        System.out.printf("Approximate sqrt of %s is %.4f\n", "f(x)=" + squareFunction.apply(initialGuess), result);
    }
}

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