What is Interpolation: Definition and 154 Discussions

In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing new data points within the range of a discrete set of known data points.In engineering and science, one often has a number of data points, obtained by sampling or experimentation, which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate, i.e., estimate the value of that function for an intermediate value of the independent variable.
A closely related problem is the approximation of a complicated function by a simple function. Suppose the formula for some given function is known, but too complicated to evaluate efficiently. A few data points from the original function can be interpolated to produce a simpler function which is still fairly close to the original. The resulting gain in simplicity may outweigh the loss from interpolation error.

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  1. Dissident Dan

    Interpolation Axis for two Matrices

    If you have two standard 3d, orthogonal matrices representing axes of 3d coordinate systems of the same handedness, is it possible to find the vector about which you would rotate one of the matrices to get the other? If so, this would be a lot more intuitive than quaternions (at least for me)...
  2. L

    Solving Linear Interpolation for 3-D Triangle Edges

    I have a 3-D traingle, and the edges are a,b,c. If I want to find a line interpolation at a point in the center, let's say that it's P(x,y)... My equations are \Delta Z = A + Bx + Cy \Delta Z_a = A + Bx_a + Cy_a \Delta Z_b = A + Bx_b + Cy_b \Delta Z_c = A + Bx_c + Cy_c In order to...
  3. M

    What is median by interpolation and how can it help me find the median?

    I was doing some last minute skimming through my book for my exam tomorrow and panic. Can someone please please tell me about finding the median by interpolation and perhaps an example of how it would could used or asked, i will be forever greatful :cool: yasmin x (i can only find a...
  4. K

    How can interpolation be used to find a polynomial formula for G(n)?

    Find a formula to calculate G(n) and it should be a polynomial of degree 4. G(n) = 1/6(0)(0-1)(0-2) + 1/6(1)(1-1)(1-2)+...+1/6(n-1)(n-2)(n-3) I know G(0)=G(1)=G(2)=G(3)=0 G(4)=1 G(5)=1+3 G(6)=1+3+6 G(7)=1+2+3+10 G(8)=1+3+6+10+15 (sum of triangle numbers) What should I do to...
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