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    so an exam question has

    2x^3 + 4x =3

    and the question suggests you use an iterative form of

    X = 3/4 - X^3 /2

    Whereas I want to use

    X= Cube root( 3/2 - 2x)


    Their suggested form settles down and mine doesnt?
    Taking a est between 0 and 1 why doesnt mine settle down?

    Jj
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    (Original post by Jon J Wood)
    so an exam question has

    2x^3 + 4x =3

    and the question suggests you use an iterative form of

    X = 3/4 - X^3 /2

    Whereas I want to use

    X= Cube root( 3/2 - 2x)


    Their suggested form settles down and mine doesnt?
    Taking a est between 0 and 1 why doesnt mine settle down?

    Jj
    Whether or not an iteration formula x = g(x) converges or diverges depends on the magnitude of g'(x) (the gradient of g(x)) near the actual root. You can find an explanation here. I don't think this is within the A level syllabus, even for further maths.
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    (Original post by Jon J Wood)
    so an exam question has

    2x^3 + 4x =3

    and the question suggests you use an iterative form of

    X = 3/4 - X^3 /2

    Whereas I want to use

    X= Cube root( 3/2 - 2x)


    Their suggested form settles down and mine doesnt?
    Taking a est between 0 and 1 why doesnt mine settle down?

    Jj
    For GCSE you will always be given the iterative formula and starting value. All you need to be aware of is that a different formula and starting value can change whether the iteration works but you don’t need to know when/why.

    Or do you know this but are still interested in when an iterative formula converges?
 
 
 
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