Numerical Analysis question.Please help!!!?

[tzanak]

Please, can you tell me what is the difference between linear,quadratic an cubic polynomial interpolation?
When we talk about these interpolations, do we usually mean the Lagrange polynomial interpolations?

Thanks!
Hans B: Thanks! So, practically, If I am given 10 points and asked to compute the linear, quadratic and cubic polynomial interpolation for a point, should I use only 2,3,4 points respectivelly?

[Hans B]

Wether its Lagrange or Newtonian or whatever interpolation will depend on the course you're taking and what your professors expect of you. For us its Newtons Polynomial Interpolation.
The difference between the linear, quadratic, cubic is simply the polynomial you're trying to find. It always depends on the points you're interpolating. If a linear equation satisfies all the points you have, you have found the linear polynomial. If a quadratic equation satisfies all your points, you have found the quadratic polynomial you're looking for. Idem for the cubic.
The important thing to remember is that you cannot find a polynomial with greater than 'n' degree for 'n' points. If you have 3 points to interpolate, you won't find a 4th degree polynomial.
Hope that helps.