How can I get all possible solutions for an equation?

Question

payman khayree 2014-8-26

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/152458-how-can-i-get-all-possible-solutions-for-an-equation

评论： payman khayree 2014-9-3

采纳的回答： Greg Heath

在 MATLAB Online 中打开

I need to get all possible solutions for this equation:

sin(x)/x == a

for "0.2 < a < 1", it has 3 to 5 solutions but matlab functions such as "solve" and "vpasolve" only return the first solution they find. How can I get all the answers? should I use another function?

thank you all payman

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Greg Heath 2014-8-27

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/152458-how-can-i-get-all-possible-solutions-for-an-equation#answer_149967

在 MATLAB Online 中打开

Some or all of the solutions can probably be obtained via recursion.

Given a, b=1/a and x(1), try

 x(n+1) = arcsin(a*x(n))
and
 x(n+1) = b*sin(x(n))

Simultaneously plotting y1= a*x and y2 = sin(x) for 0.2 <= a <= 1 will yield insight.

Hope this helps.

Thank you for formally accepting my answer

Greg

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

payman khayree 2014-9-3

not what I was looking for, but anyways thanks for your answers

请先登录，再进行评论。

Answer 2

John D'Errico 2014-8-26

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/152458-how-can-i-get-all-possible-solutions-for-an-equation#answer_149926

All possible solutions is in general an impossible thing for a completely general function, since there may be infinitely many such solutions.

If you know there are a finite number of solutions, and can bound them, then just sample your function on a fine enough interval, and use fzero over brackets generated by the sampling. WTP?