使用20项计算sin（x）的近似值

Question

我试图用泰勒近似来评估1.89的sin的近似值。我将输出与Math.sin（x）的值进行了比较;然而，在大约14个术语之后，我的价值偏离很大并且变得错误。我尝试了x的较小值（< 0.5）的近似值，并且这些值相匹配。

我只是想弄清楚为什么在Mac OSx上使用崇高和通过bash编译的Java偏离了真正的输出。

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

的原因是在这里：

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

你是不是在考虑到阶乘收敛速度非常快产生溢出（有些结果是那么负数）

可以验证BEH 。拆分一点在使用阶乘返回值的代码：

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); 
      } 
     } 

，你会注意到，输出会产生被distroying你想要达到的数值逼近负值

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

Answer 2

建议使用BigDecimal而不是double和int进行大数值计算，如阶乘和功率。