Question

我试图使用泰勒近似来评估1.89的sin的近似值。我将输出与Math.sin（x）中的值进行了比较;然而，在大约14个学期之后，我的价值偏差很大并且变得错误。我尝试了较小的x（<0.5）值的近似值，并且值匹配。

我只想弄清楚为什么Java，使用sublime并在Mac OSx上通过bash进行编译会偏离真正的输出。

public class Test {

    public static void main (String[] args) {
        double x = 1.89;
        double sinx = 0;
        int n = 20;
        int countOdd = 1;
        int counter = 1;
        int result = 0;
        int value = 0;

        while (countOdd <= n) {
            if (counter%2 != 0) {
            // Even term odd number
                if (countOdd%2 == 0) {
                    sinx = sinx - (Math.pow(x,counter)/(double)factorial(counter));
                    System.out.println(" counter even odd term  = " + countOdd);
                    countOdd++;
                    System.out.println(" sinx  = " + sinx);
                }
                // Odd term odd number
                else {
                    sinx = sinx + (Math.pow(x,counter)/(double)factorial(counter));
                    System.out.println(" counter odd odd term  = " + countOdd);
                    countOdd++;
                    System.out.println(" sinx  = " + sinx);
                }
            }
            // Update the result and reset the value
            //sinx = sinx + value;
            //value = 0;
            System.out.println(" counter  = " + counter);
            counter++;
        }

        System.out.println(" sinx  = " + sinx);
        System.out.println(" sinx from math library = " + Math.sin(x));
    }

    /** calcutes and returns  n! 
    @param n : a positive integer number
    @return n!
    */
    public static int factorial(int n)
    {
        // your code goes here
        int result = 1; // if n = 0, while loop is by passed and 0 is returned
        while (n >= 1) {
            result = result * (n);
            n--;
        }

        return result;
    }
}

Answer 1

建议使用BigDecimal代替double和int进行大数值计算，例如阶乘和幂。

Answer 2

原因在于：

public static int factorial(int n) {
    int result = 1;
    while (n >= 1) {
        result = result * (n);
        n--;
    }
    return result;
}

你没有考虑这样一个事实：阶乘收敛非常快，产生溢出（有些结果是负数）

你可以验证那个。拆分使用factorial返回值的代码：

    while (countOdd <= n) {

        if (counter % 2 != 0) {
            // Even term odd number
            if (countOdd % 2 == 0) {
                int factorial = factorial(counter);
                System.out.println("factorial: " + factorial);
                sinx = sinx - (Math.pow(x, counter) / factorial);
                System.out.println(" counter even odd term  = " + countOdd);
                countOdd++;
                System.out.println(" sinx  = " + sinx);
            }
            // Odd term odd number
            else {
                int factorial = factorial(counter);
                System.out.println("factorial: " + factorial);
                sinx = sinx + (Math.pow(x, counter) / factorial);
                System.out.println(" counter odd odd term  = " + countOdd);
                countOdd++;
                System.out.println(" sinx  = " + sinx);
            }
        }

正如您将注意到的，输出将产生负值，这会破坏您想要实现的数值近似值

 ...
 counter even odd term  = 10
 sinx  = 0.9476740866450655
 counter  = 19
 counter  = 20
 factorial: -1195114496

使用20项计算sin（x）的近似值

2 个答案: