Thread Subject:

Smallest real positive root

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.

"Robert Maxim" <toejama1@gmail.com> wrote in message <hqgd7l$t74$1@fred.mathworks.com>...
> 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.

Sorry, but um, no.

John

"Robert Maxim" <toejama1@gmail.com> wrote in message <hqgd7l$t74$1@fred.mathworks.com>...
> 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.
----------------
  Could you please go into greater detail regarding that phrase "something I am casting a ray with"?

Roger Stafford

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.

"Roger Stafford" <ellieandrogerxyzzy@mindspring.com.invalid> wrote in message <hqgdu5$c5c$1@fred.mathworks.com>...
> "Robert Maxim" <toejama1@gmail.com> wrote in message <hqgd7l$t74$1@fred.mathworks.com>...
> > 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.
> ----------------
> Could you please go into greater detail regarding that phrase "something I am casting a ray with"?
>
> Roger Stafford

"Robert Maxim" <toejama1@gmail.com> wrote in message <hqged6$jt8$1@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

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.

intersection point for a curve surface from a ray cast quickly and accurately

"Roger Stafford" <ellieandrogerxyzzy@mindspring.com.invalid> wrote in message <hqgfin$95c$1@fred.mathworks.com>...
> "Robert Maxim" <toejama1@gmail.com> wrote in message <hqged6$jt8$1@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