Re: solving the equation

On Jan 30, 10:01 am, "Greg Neill" <gneil...@xxxxxxxxxxxxxxxx> wrote:
Nimo wrote:
yeah, once again thanks for the questions,
I hope I'll answer them briefly for you.

1. How many separate constraint equations (points) are you expecting
   to have to deal with?
2. Is your method to be automated on a computer or worked by hand
   each time?
3. Do you have a predetermined knowledge of what form F(x) might take?
   (exponential, polynomial, logarithmic, trigonometric...)?
4. How accurately does your F(x) have to match your initial points?
   In other words, what is your error tolerance?

Ans_1) many,
       think like this If this is the equation
       Integral 0_n f(x) dx = p, so total
       constraints are 'n'

And how large is n expected to be?



Ans_2) both, I've to deal both of the cases exclusively
       If I'm right you are thinking to advise
       me to use any Numerical Solution technique
       considering it as a ODE,on a computer.
       but that is not the exact case.

No, for reasonable sized systems you can use computer algebra
systems or "infinite" precision math systems to give rational
results.  No ODE's involved.



Ans_3) no,I don't know anything thing about f(x)
       other than the provided data like in the
       post_1.

If you have the provided data then you can *look* at them
plotted and get an idea of the type of function they resemble.

If you really have no idea about the nature of the function
or its order, and if you want an exact fit to all possible
sets of points, then you have no choice but to go with the
similarly high degree polynomial, if a polynomial solution
is required.



Ans_4) There is no question of 'ERROR'.
_______
" I think we understand the problem you stated, but what is not
clear is in what context is it to be set?  Is it purely a
hypothetical question or is it predicated on some real-world
requirement? "

here, how do you differentiate a problem
"whether it is Hypothetical or real-world problem"
if you provide me more information,I hope I can make you
crystal clear.

(!)



________
" They are not necessarily linear functions.  They are linearly
independent functions, which means that no linear combination
(sum, difference, scale) operations on a subset of the functions
will yield one of the functions not in that subset.

An example set might be the polynomials:

(1, x, x^2, x^3, x^4, ... ,x^n) "

OKAY.., now this doubt is clarified
thanks for you :)
_________
"
40 or 50 points is a trivial size for a computer to handle.
So again, what is determining your complexity threshold?"

I don't want the solution be a polynomial of higher degrees(k)

Then use some other basis set of functions.

For example, if the number of data points is a power of 2
you can take a Fourier transform of it to create a sine
and cosine function representation which can then be
differentiated to give you your function.  In that way
you can trade polynomial complexity for series length.

__________
"
Your problem statement, so far, has not been provided with
any context.  We don't know where the data points come from,
what tools you have on hand to implement a solution, or what
the solution will be used for "

tools,
solution technique,and other stuff
you people have to suggest me

We are supposed to suggest to you where your problem comes from
and in what context it arose?  How can we do that?

----
Thank_you :) for the clarifications,
just I need 30-to-60 minutes time, I'm checking this question
with my peers and I'll state about it everything clearly,
with out any confusion,
this time while stating the question I'll be more clear
because in the previous replies I had already *experienced*
the magnitude of difficulties we have to face, because of the
lack of clarity.Keeping all this in my mind.I'll come up with in an
Hr or so.

Any how these are the conclusions,
I want to draw from all the replies I got
Conclusions:-
a) Any straight line or a parabola or any curve except (exact
polynomial)
can't pass through all our points.
b) a function of ONE variable is *nothing* to solve this problem.

I hope, now every one is quite familiar with my problem(I'm very
happy about that, at_least in the sense that users had understand what
my
problem is exactly?).
Always my question will be the same(see the post_1)
but that's the exact one, its time to do some modifications for it.

I want to conclude all this things from all you people's help,
instead of that,
If I didn't tell you all these things and keep asking you about
2 variable functions or any other stuff, users will be totally
confused :(

Once they are familiar with my basic difficulties,they can help me
to over come the difficulties I've to face in the next question.

Thank_you :)
I'm coming....!

.

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