Re: solving the equation

On Jan 30, 12:45 am, "Greg Neill" <gneil...@xxxxxxxxxxxxxxxx> wrote:
Nimo wrote:
first of all thanks :) for the reply
yes, I can understand your points
sorry for the confusion, I'll answer each and every point of
your's neatly with out any confusion.

your 3 questions are like this

a) what is my problem.....?
b) page for Vandermonde matrix......?
c) completion of my problem statement clearly...?

Those weren't my questions precisely.  Here they are:

Some questions:

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?

You've answered (4): you require an exact fit, although you did
not state why this is a requirement, and you have not explicitly
stated whether all the points are required to make a fit; the
actual curve may be oversampled.  For example, suppose the "real"
curve was a quadratic of the form a0 + a1*x + a2*x^2 but you
happen to have 147 sample points.  Would it make sense to try to
fit all of the points to a degree 147 polynomial only to find
out that all the coefficients a3...a147 are zero?  This is why my
question (3) is relevant.

Your new statements/questions are also pertinent:



lets see I'll answer to your questions clearly

Ans a) I'll not write all the stuff here,please
       read the first post of mine
       for that question most of the people
       helped me with suggestions like
       polynomial,linear_algebra and etc,etc..

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?



but, one particular suggestion I got from
Dr.Robert sir is like this 5th post from top
"
a f_1(x) + ... + e f_5(x) where f_1, ..., f_5 are linearly
independent functions. "

I think this would be helpful for me, but my doubt is
how to take the linear functions f_1(x),f_2(x),...f_n(x)

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)

which is the set that most people have been suggesting.  But
you could choose some other set of linearly independent functions,
such as the Bessel functions, or some set of trig functions.



for this technique I'm looking everywhere.

coming to the second question

Ans b) you have provided me Vandermonde matrix page
       thanks for that, yes I've very huge volume of numbers
       say for example 40,50..like so
       it's not the question of implementing that technique
       but at the end I'll get a polynomial of higher
       degree, which I'm not interested basically.

40 or 50 points is a trivial size for a computer to handle.
So again, what is determining your complexity threshold?

coming to 3rd one

Ans c) completion of my problem statement clearly...?
       Right from starting I keep on repeating that
       I'll have Integral_equations like in the first post
       (please see it) and constraints too are provided
       along with it, so that at the end for a function f(x)
       on integrating subject to the boundary conditions
       I want my value back.
      that's it

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.



I hope I've made you clear with out any confusion,
if I didn't make you clear, please,please ask them
I'll provide more & more details

Thanks for the help :)



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'

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.

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

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)
__________
"
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
_______________
.

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