Iteration functions for Fixed Point method

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SUMMARY

The discussion focuses on finding iteration functions for the equation x - 2sin(x)/cos(x) = 0. The initial function g(x) = 2sin(x)/cos(x) was identified as non-convergent. Alternative iteration functions proposed include g(x) = arcsin(x cos(x)/2), g(x) = arccos(2 sin(x)/x), and g(x) = arctan(x/2), which effectively isolate x on one side of the equation.

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  • Knowledge of trigonometric functions and their inverses
  • Familiarity with convergence criteria in numerical methods
  • Basic calculus concepts related to function behavior
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carlosbgois
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Hi there. I need to find some iteration functions for [itex]x - 2\frac{sin(x)}{cos(x)}=0[/itex], as [itex]g(x)=2\frac{sin(x)}{cos(x)}[/itex] does not converge. I can't find any others, maybe I didn't quite undertood how they're built. Any help will be appreciated

Thanks
 
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You could check [itex]g(x)=arcsin(\frac{x \cos(x)}{2})[/itex] and [itex]g(x)=arccos(\frac{2 \sin(x)}{x})[/itex] and g(x)=arctan(x/2)? That is just your formula, with different ways to isolate an x at one side.
 

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