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Thread: (quadratic) convergence

  1. #1 (quadratic) convergence 
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    1) Is , in principle, oscillating convergence more efficient than monotonic?
    If not particularly so, it is always better anyway, as it gives you a rough idea where your root is from the beginning

    2) They say that Newton's algorithm has quadratic convergence, can one determine that a priori examining the formulas (through f''(x)) or you must take a few calculations?

    If we compare the results , applying the formula for square and cube root, we see that : if the root (L) is 1,000 and we start from 10,000
    a) for [(x+a):2x] the values decrease (roughly) by 1/2: 10000, 5050, 2600, etc
    b) for [(2x+a):3x] they decrease by 1 /3

    Is convergence quadratic in both cases? can you show me how you prove that?
    3) what is the correct term for these series: monoton(ic) decreasing

    4)) is it difficult to change a formula so that the convergence is oscillating?

    is there a general principle that makes a convergence oscillate? Can you give me some examples of oscillating (quadratic) formulas?

    Thanks


    Last edited by logic; April 27th, 2012 at 07:30 AM.
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