parabolic interpolation between 3 nearest points
sk maidul haque
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.
Matt J
> 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.
Roger Stafford
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
sk maidul haque
>>>>>>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.