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Topic: Root
Replies: 21   Last Post: Jul 14, 1999 3:46 PM

 Messages: [ Previous | Next ]
 carel Posts: 161 Registered: 12/12/04
Re: Root
Posted: Jul 11, 1999 9:42 AM

The method of Newton is very elegant to solve for roots

Let f(x) = x^2 - A where A is the number to get the square root from.

Then g(x) = f'(x) = 2x

Then xnew = xold - f(xold)/g(xold) = xold - [xold^2 - A]/[2xold]

So guess a value for x and then obtain a new guess value.

You will soon obtain x = A^(.5)

In general you can obtain any root by letting f(x) = x^n - A and g(x) =
nx^(n-1)

Carel
>James Adelman wrote on 11 Jul 99 12:57:39 +0000 in sci.math:
>

>> Kaimbridge wrote on Sun, 11 Jul 1999 08:52:29 GMT in sci.math:
>>

>> > In article <k4Ph3.7360\$Le1.136634@news2.randori.com>,
>> > "User" <pohanl@aol.com> wrote:

>> > >
>> > > Does anyone know how to go about doing a square root or cube root
>> > > calculation?

>> >
>> > There was a good post on "the hand method" done back in January:
>> >
>> > http://www.deja.com/=dnc/getdoc.xp?AN=433077696
>> >
>> > ~Kaimbridge~
>> >

>> An alternative might be to use the binomial expansion, although this
>> will probably make for a lot more arithmetic than the one at the
>> URL above; it _may_ need fewer terms for accuracy, but I don't think
>> so, you's have to try it.
>>
>> Let's try 57:
>>
>> 57^.5=49^.5*(57/49)^.5
>> =7*(1+8/49)
>>

>Missed some brackets: should be
>
>

=7*[(1+(1/2)(8/49)+(1/2)(-1/2){(8/49)^2}/2+(-3/2)(-1/2)(1/2){(8/49)^3}/3!+..
.]
>>
>> It works, but without a calculator (or even with one) it requries lots
>> of effort. I suppose the only good news is the factorial on the
>> bottom.
>>

>> > --
>> > Note that "news" in "@my-dejanews.com" has been
>> > dropped.
>> >
>> >
>> > Sent via Deja.com http://www.deja.com/
>> > Share what you know. Learn what you don't.

>>
>> --
>>

>
>--
>

Date Subject Author
7/10/99 User
7/10/99 Prasanth A. Kumar
7/11/99 William L. Bahn
7/11/99 Kaimbridge
7/11/99 carel
7/11/99 chri0562@sable.ox.ac.uk
7/11/99 spamless@nil.nil
7/12/99 test@test.com
7/14/99 Chris J. Bennardo
7/12/99 John Popelish
7/12/99 philnovi
7/12/99 Ken Cox
7/12/99 randy
7/13/99 John Savard
7/13/99 Paul J. Gans
7/13/99 Jack Silver
7/13/99 Paul Schlyter
7/13/99 philnovi
7/12/99 Gareth McCaughan
7/12/99 randy