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Thread Subject:
parabolic interpolation between 3 nearest points

Subject: parabolic interpolation between 3 nearest points

From: sk maidul haque

Date: 26 Jun, 2011 07:05:04

Message: 1 of 4

Can somebody please explain me what does it mean by 'parabolic interpolation between 3 nearest points' . Does it mean that a parabola is to be ploted between 3 points which are nearest to the concerned point where I want to do the interpolation and then to calculate the value from the equation of parabola at concerned point.
If it is so, then what is the form of equation of parabola to be used ?

what is the related command in matlab to do parabolic interpolation between specified number of nearest neighbour points.

Thanks in advance.

Subject: parabolic interpolation between 3 nearest points

From: Matt J

Date: 26 Jun, 2011 12:04:05

Message: 2 of 4

"sk maidul haque" <skmaidulhaque@gmail.com> wrote in message <iu6ln0$1n6$1@newscl01ah.mathworks.com>...
> Can somebody please explain me what does it mean by 'parabolic interpolation between 3 nearest points' . Does it mean that a parabola is to be ploted between 3 points which are nearest to the concerned point where I want to do the interpolation and then to calculate the value from the equation of parabola at concerned point.
==============

What it means will only be clear once you elaborate for us on what it is you are trying to accomplish. For example, parabolic interpolation sometimes refers to a way of minimizing a 1D function

http://en.wikipedia.org/wiki/Successive_parabolic_interpolation

but who knows if that's applicable to you.

Subject: parabolic interpolation between 3 nearest points

From: Roger Stafford

Date: 26 Jun, 2011 19:51:04

Message: 3 of 4

"sk maidul haque" <skmaidulhaque@gmail.com> wrote in message <iu6ln0$1n6$1@newscl01ah.mathworks.com>...
> Can somebody please explain me what does it mean by 'parabolic interpolation between 3 nearest points' . Does it mean that a parabola is to be ploted between 3 points which are nearest to the concerned point where I want to do the interpolation and then to calculate the value from the equation of parabola at concerned point.
> If it is so, then what is the form of equation of parabola to be used ?
>
> what is the related command in matlab to do parabolic interpolation between specified number of nearest neighbour points.
>
> Thanks in advance.
- - - - - - - - - -
  Assuming your interpretation is the one to be used, let (x1,y1), (x2,y2), and (x3,y3) be the three "nearest" points and (x,y) be the "concerned" point. If (x,y) is to lie on the parabola through the three points, you can express y as a quadratic function of x in the form:

 y = a*(x-x2)^2 + b*(x-x2) + y2

where a and b are:

 a = ((y3-y2)/(x3-x2)-(y2-y1)/(x2-x1))/(x3-x1)
 b = ((y3-y2)/(x3-x2)*(x2-x1)+(y2-y1)/(x2-x1)*(x3-x2))/(x3-x1)

  An alternative would be to use Lagrange's interpolation method for second degree polynomials. See

 http://en.wikipedia.org/wiki/Lagrange_polynomial

Roger Stafford

Subject: parabolic interpolation between 3 nearest points

From: sk maidul haque

Date: 27 Jun, 2011 08:52:02

Message: 4 of 4

"Roger Stafford" wrote in message <iu82j8$gun$1@newscl01ah.mathworks.com>...
> "sk maidul haque" <skmaidulhaque@gmail.com> wrote in message <iu6ln0$1n6$1@newscl01ah.mathworks.com>...
> > Can somebody please explain me what does it mean by 'parabolic interpolation between 3 nearest points' . Does it mean that a parabola is to be ploted between 3 points which are nearest to the concerned point where I want to do the interpolation and then to calculate the value from the equation of parabola at concerned point.
> > If it is so, then what is the form of equation of parabola to be used ?
> >
> > what is the related command in matlab to do parabolic interpolation between specified number of nearest neighbour points.
> >
> > Thanks in advance.
> - - - - - - - - - -
> Assuming your interpretation is the one to be used, let (x1,y1), (x2,y2), and (x3,y3) be the three "nearest" points and (x,y) be the "concerned" point. If (x,y) is to lie on the parabola through the three points, you can express y as a quadratic function of x in the form:
>
> y = a*(x-x2)^2 + b*(x-x2) + y2
>
> where a and b are:
>
> a = ((y3-y2)/(x3-x2)-(y2-y1)/(x2-x1))/(x3-x1)
> b = ((y3-y2)/(x3-x2)*(x2-x1)+(y2-y1)/(x2-x1)*(x3-x2))/(x3-x1)
>
> An alternative would be to use Lagrange's interpolation method for second degree polynomials. See
>
> http://en.wikipedia.org/wiki/Lagrange_polynomial
>
> Roger Stafford

>>>>>>Thanks.
but then what will be the corresponding equation if the parabolic interpolation is to be made between 4 nearest points instead of 3.
Is it going to be of the form
y = a*(x-x2)^3 + b*(x-x2)^2 + c*(x-x2)+ y2

where
a=..........
b=............
c=............

If it is so, then what is the difference between parabolic interpolation and polynomial interpolation.

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