我已经为Fortran中的二分法编写了以下代码，但是在满足我在Do While循环中定义的条件后它并没有停止。任何解释都将不胜感激。
! Bi-section method
program bi_section
implicit none
!Variables
real :: a, b, p
real :: fa, fb, fp, fc
! Interval
a = 2.0
b = 3.0
! Value of fa & fb
fa = a*a*a-13
fb = b*b*b-13
do while (abs(fb-fa) > 0.00001)
p = (a+b)/2
fp = p*p*p-13
if (fp*fa > 0) then
a = p
else
b = p
end if
print*, p
enddo
end program bi_section
答案 0 :(得分：2)
要找到可能的错误，一个好的方法是打印相关变量的值（例如a，b，fa和fb）并检查是否事情正如预期的那样。例如，
do while (abs(fb-fa) > 0.00001)
p = (a+b)/2
fp = p*p*p-13
if (fp*fa > 0) then
a = p
else
b = p
end if
!-- print*, p
print*, p, a, b, fa, fb !<--- print more variables for check
enddo
上面的print语句给出了
2.50000000 2.00000000 2.50000000 -5.00000000 14.0000000
2.25000000 2.25000000 2.50000000 -5.00000000 14.0000000
2.37500000 2.25000000 2.37500000 -5.00000000 14.0000000
2.31250000 2.31250000 2.37500000 -5.00000000 14.0000000
2.34375000 2.34375000 2.37500000 -5.00000000 14.0000000
2.35937500 2.34375000 2.35937500 -5.00000000 14.0000000
2.35156250 2.34375000 2.35156250 -5.00000000 14.0000000
2.34765625 2.34765625 2.35156250 -5.00000000 14.0000000
2.34960938 2.34960938 2.35156250 -5.00000000 14.0000000
2.35058594 2.35058594 2.35156250 -5.00000000 14.0000000
2.35107422 2.35107422 2.35156250 -5.00000000 14.0000000
2.35131836 2.35131836 2.35156250 -5.00000000 14.0000000
2.35144043 2.35131836 2.35144043 -5.00000000 14.0000000
2.35137939 2.35131836 2.35137939 -5.00000000 14.0000000
2.35134888 2.35131836 2.35134888 -5.00000000 14.0000000
2.35133362 2.35133362 2.35134888 -5.00000000 14.0000000
2.35134125 2.35133362 2.35134125 -5.00000000 14.0000000
2.35133743 2.35133362 2.35133743 -5.00000000 14.0000000
2.35133553 2.35133362 2.35133553 -5.00000000 14.0000000
2.35133457 2.35133457 2.35133553 -5.00000000 14.0000000
2.35133505 2.35133457 2.35133505 -5.00000000 14.0000000
...
所以，尽管p正在接近正确的解决方案（13的立方根= 2.3513346 ......），fa和fb都不会改变，“条件”（{永远不会遇到{1}}）（正如评论中@HighPerformanceMark所建议的那样）。为避免这种情况，我们需要更新abs(fb-fa) <= 0.00001和fa，例如
fb给出了
do while (abs(fb-fa) > 0.00001)
p = (a+b)/2
fp = p*p*p-13
if (fp*fa > 0) then
a = p
fa = fp !<---
else
b = p
fb = fp !<---
end if
print*, p, a, b, fa, fb
enddo
（顺便说一句，我们可以将 2.50000000 2.00000000 2.50000000 -5.00000000 2.62500000
2.25000000 2.25000000 2.50000000 -1.60937500 2.62500000
2.37500000 2.25000000 2.37500000 -1.60937500 0.396484375
2.31250000 2.31250000 2.37500000 -0.633544922 0.396484375
2.34375000 2.34375000 2.37500000 -0.125396729 0.396484375
2.35937500 2.34375000 2.35937500 -0.125396729 0.133815765
2.35156250 2.34375000 2.35156250 -0.125396729 3.77845764E-03
2.34765625 2.34765625 2.35156250 -6.09159470E-02 3.77845764E-03
2.34960938 2.34960938 2.35156250 -2.85959244E-02 3.77845764E-03
2.35058594 2.35058594 2.35156250 -1.24149323E-02 3.77845764E-03
2.35107422 2.35107422 2.35156250 -4.32014465E-03 3.77845764E-03
2.35131836 2.35131836 2.35156250 -2.70843506E-04 3.77845764E-03
2.35144043 2.35131836 2.35144043 -2.70843506E-04 1.75380707E-03
2.35137939 2.35131836 2.35137939 -2.70843506E-04 7.41004944E-04
2.35134888 2.35131836 2.35134888 -2.70843506E-04 2.35557556E-04
2.35133362 2.35133362 2.35134888 -1.71661377E-05 2.35557556E-04
2.35134125 2.35133362 2.35134125 -1.71661377E-05 1.08718872E-04
2.35133743 2.35133362 2.35133743 -1.71661377E-05 4.48226929E-05
2.35133553 2.35133362 2.35133553 -1.71661377E-05 1.33514404E-05
2.35133457 2.35133457 2.35133553 -1.90734863E-06 1.33514404E-05
2.35133505 2.35133457 2.35133505 -1.90734863E-06 6.67572021E-06
写为p*p*p-13）。