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<div class="moz-cite-prefix">The eps value is the smallest number
that you can add to one and get a value different from one. In
IEEE 64 bit precision that is <img style="vertical-align: middle"
src="cid:part1.03080300.03050803@mercer.edu"
alt="$\frac{1}{2}^{52}$">. The other number you mention is the
smallest number representable in the IEEE double precision format.<br>
<br>
Remember -- in machine numbers you have a sign, an exponent, and a
mantissa. If you are doing tolerance calculations in some way or
another you are really only considering values in the mantissa --
they may be scaled by the exponent -- but ultimately any tolerance
you set will have to be equal to the eps (which is problematic) or
related to it somehow greater. The common custom is to set a
tolerance that is greater than the eps. The problem is how to
evaluate if you have achieved that tolerance. I look forward to
seeing what you come up with for that.<br>
<br>
<br>
<br>
<br>
On 09/14/13 19:14, \ wrote:<br>
</div>
<blockquote
cite="mid:C40B2F181831EF44A88CD73525827803026514AC73@MERCERMAIL.MercerU.local"
type="cite">
<pre wrap="">Hi Dr. Pounds,
I've been working on implementing the bisection method and for some
reason the smallest tolerance, using doubles, for (b - a) / 2 that I
can achieve is 10^ -15. I know that this is the level of precision
that can usually be achieved using double precision, but isn't the
minimum value what should be limiting me? And isn't that minimum value
something like 10^ -304 (i.e. much, much smaller than 10^ -15).
Thanks,
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</blockquote>
<br>
<br>
<pre class="moz-signature" cols="72">--
Andrew J. Pounds, Ph.D. (<a class="moz-txt-link-abbreviated" href="mailto:pounds_aj@mercer.edu">pounds_aj@mercer.edu</a>)
Professor of Chemistry and Computer Science
Mercer University, Macon, GA 31207 (478) 301-5627
<a class="moz-txt-link-freetext" href="http://faculty.mercer.edu/pounds_aj">http://faculty.mercer.edu/pounds_aj</a>
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