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Chebyshev

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  • javiergijn
    Hello all: I would like to know if someone has used Chebyshev correction for square root aproximation. In that case , whats your opinion about it ? Chebyshev
    Message 1 of 8 , Feb 1 12:28 PM
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      Hello all:
      I would like to know if someone has used Chebyshev correction
      for square root aproximation.
      In that case , whats your opinion about it ?

      Chebyshev correction is explained on Ron´s book and, as you now
      , the expression for square root is : (1/8*an)* ((N-an^2)/an)^2 ,

      Where N is the number we want to obtain the square root of,
      an the n-aproximation.

      Ron , what about 6 * 6 ? . 4 * 4 digits was great.


      Best wishes to all.

      Javier.
    • George Lane
      Hi Oleg Yes, it would be relatively easy to divide 11730 by 10 and look at 1173, but my reason for treating the problem as I did is this: When competing in the
      Message 2 of 8 , Feb 2 11:24 AM
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        Hi Oleg

        Yes, it would be relatively easy to divide 11730 by 10 and look at 1173, but my reason for treating the problem as I did is this:

        When competing in the Mental Calculations World Championships, the prime factors problems have to be solved with the prime factors themselves given in ascending numerical order. If I had originally divided by 10 and then checked for the factors of 1173, the factor of 3 would have appeared out of order. However, if a brief check had revealed no factors of 3 in the number, then it would be better to divide by 10 to begin with - and, of course, to record one factor each of 2 and 5.

        Best regards,
        George Lane

        Oleg Stepanov <olegstepanov@...> wrote:
        GL> Sample problem: Find the prime factors of 11730
        GL> 11730/2=5865, which is not divisible by 2
        GL> 5865/3=1955 which is not divisible by 3
        GL> 1955/5=391 which is not divisible by 5, 7, 11 or 13
        GL> 391/17=23 which is a prime number
        GL> The list of prime factors is thus 2, 3, 5, 17, and 23.

        Please, I fill myself little strange. Probably I do not understand
        something. Why not divide on 10 and by looks full number 11730 think
        only about 1173? Your method remind me Jededia Buxton what by multiple
        on 300 made it by 5, 20 and 3.
        Apologize if I am not correct or did not find explanation...


        Sincerely Yours Oleg Stepanov.

        http://www.lk.net/~stepanov/






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      • Oleg Stepanov
        Sure future champion. :-) http://www.ruediger-gamm.de/ Sincerely Yours Oleg Stepanov. http://www.lk.net/~stepanov/
        Message 3 of 8 , Feb 7 4:28 PM
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          Sure future champion. :-)
          http://www.ruediger-gamm.de/



          Sincerely Yours Oleg Stepanov.

          http://www.lk.net/~stepanov/
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