How can I get all possible solutions for an equation?
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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
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Greg Heath
2014-8-27
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
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John D'Errico
2014-8-26
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?
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