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From: Walter Roberson on 18 Apr 2010 23:37
Robert Maxim wrote:
> Is there a quick way in matlab to give me the smallest possible real
> root of something I am casting a ray with. Newtons, seecannt are too slow.

Let me introduce you to the many many decades of work it took to
determine whether Riemann's Zeta function _has_ a real root or not.

There are a lot of functions whose smallest root is unknown and the
question of what the smallest root _is_, is of quite a bit of
speculation. Functions which may or may not have a known large root
("upper bound on the value") but where the lower bound on the value
might be undetermined. There's a famous example in mathematics where a
mathematician proved an upper bound on a limit which is the largest
number ever non-trivially used in a mathematical theorem (a new notation
had to be invented to express it)... it is commonly believed that the
actual smallest root for the problem is 6, but no-one has been able to
_prove_ a smaller lower bound than the largest number ever expressed.
From: Robert Maxim on 19 Apr 2010 00:04
intersection point for a curve surface from a ray cast quickly and accurately

"Roger Stafford" <ellieandrogerxyzzy(a)mindspring.com.invalid> wrote in message <hqgfin$95c$1(a)fred.mathworks.com>...
> "Robert Maxim" <toejama1(a)gmail.com> wrote in message <hqged6$jt8$1(a)fred.mathworks.com>...
> > I want to cast a ray and find the smallest root where it intersects a surface.
> > you can easily do this with Newtonns method or Seecant but takes forever to converge and you need a good intervals.
> ---------------
> By slow tortuous degrees we are managing to extract more information from you about your question, but much more needs to be made clear. Where you say, "cast a ray and find the smallest root where it intersects a surface", is this ray being "cast" from a fixed point above a three-dimensional surface? What is known about the direction of "casting". What is the mathematical form of the surface? What quantity is it you are wishing to find the root of? - the distance to the intersection, the point of intersection? If we don't find out such things as this you may have to be content with John's succinct answer.
>
> Roger Stafford
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