Thanks for your offer. The function above was only a test case, but I had
requests where it was necessary to return zeros exactly in double
precision. I solved this -- for the test and other functions -- utilizing
the 'mpfr' software for arbitrary precision. Actually, Ridders' method can
be app
On Monday, 24 February 2014 11:34:22 UTC, Hans W Borchers wrote:
>
> This innocent looking test function appears to be so flat that only an
> arbitrary precision solver will locate this root more exactly.
>
I think what is required in this case is a more accurate implementation of
the function
Well, functions like `x -> exp(-x^3)-1` or `x -> (x^3 + 1) - 1` have
obvious roots. The root of the test function above is not that obvious. To
tell the rest of the story: I once tried to symbolically solve it with
Mathematica
Mathematica> Solve[Log[x] + x*x/(2*Exp[1]) - 2*x/Sqrt[Exp[1]] +
On Monday, February 24, 2014 8:16:28 PM UTC-8, Stefan Karpinski wrote:
>
> This sort of comparison seems inevitably bound to favor bisection for
> objective functions that are fast to evaluate and to favor "sophisticated"
> methods when the objective function is costly, no?
>
Yes, that's right.
This sort of comparison seems inevitably bound to favor bisection for
objective functions that are fast to evaluate and to favor "sophisticated"
methods when the objective function is costly, no?
On Mon, Feb 24, 2014 at 11:01 PM, Jason Merrill wrote:
> On Monday, February 24, 2014 7:48:50 PM UT
On Monday, February 24, 2014 7:48:50 PM UTC-8, Jason Merrill wrote:
>
> On Monday, February 24, 2014 3:34:22 AM UTC-8, Hans W Borchers wrote:
>
>> BTW It would be nice to have Ridders' algorithm available in Julia, too,
>> about which the "Numerical Recipes" say:
>>
>> "*In both reliability and s
On Monday, February 24, 2014 3:34:22 AM UTC-8, Hans W Borchers wrote:
>
> The following function is one of the most difficult test functions for
> univariate root finding I know of,
>
> julia> function fn(x::Real)
>return log(x) + x^2/(2*exp(1)) - 2 * x/sqrt(exp(1)) + 1
>
The following function is one of the most difficult test functions for
univariate root finding I know of,
julia> function fn(x::Real)
return log(x) + x^2/(2*exp(1)) - 2 * x/sqrt(exp(1)) + 1
end
whose exact root between 1.0 and 3.4 is sqrt(e) = 1.6487212707001282...
You can change rounding mode
with http://docs.julialang.org/en/latest/stdlib/base/#Base.set_rounding
kl. 08:16:20 UTC+1 mandag 24. februar 2014 skrev Jason Merrill følgende:
>
> Thanks for the kind words.
>
> Is the goal of the linked float range code to make things like
> `1.0:1/n:2.0` work mor
Thanks for the kind words.
Is the goal of the linked float range code to make things like
`1.0:1/n:2.0` work more reliably? Seems like a nice approach.
On Sunday, February 23, 2014 10:28:24 AM UTC-8, Stefan Karpinski wrote:
>
> This is a lovely blog post. I've given a few talks on floating-point
Thanks for the reference. I enjoyed this quite a bit--both the writing and
the content. Where would we be without Kahan?
Kahan seems to get a lot of mileage out of running programs with directed
rouding. Does Julia provide a way to set floating point rounding modes?
I'm curious why you feel Mul
Also, thought this would be of general interest on Hacker News, so I
submitted it: https://news.ycombinator.com/item?id=7286926.
On Sun, Feb 23, 2014 at 1:28 PM, Stefan Karpinski wrote:
> This is a lovely blog post. I've given a few talks on floating-point
> arithmetic using Julia for live codin
This is a lovely blog post. I've given a few talks on floating-point
arithmetic using Julia for live coding and demonstrations. The fact that
there is a next and previous floating point number – with nothing in
between – always blows people's minds, even though this is an immediate and
fairly obvio
Great post!
It may interest you that William Kahan has written quite extensively
on the pitfalls of iterative algorithms on floating point numbers; his
discussion of Muller's pathological recurrence on pp. 14+ of this
paper seems particularly relevant.
http://www.cs.berkeley.edu/~wkahan/Mindless.
This is really great material, Jason. Are you using MathJax? For me, the
LaTeX-like code doesn’t seem to get processed.
— John
On Feb 22, 2014, at 5:52 PM, Jason Merrill wrote:
> I'm working on a series of blog posts that highlight some basic aspects of
> floating point arithmetic with examp
I'm working on a series of blog posts that highlight some basic aspects of
floating point arithmetic with examples in Julia. The first one, on
bisecting floating point numbers, is available at
http://squishythinking.com/2014/02/22/bisecting-floats/
The intended audience is basically a version
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