Interpolation of measured data

I have a measured data set (x & y are inputs, z is the result at those measures):

x y z

0.036802 0.004908 0.07158

0.036802 0.022135 0.10095

0.130886 0.004908 0.09627

0.130886 0.022135 0.12560

I would like a formula for interpolation, to predict z for all input conditions x & y (within bounds), for example when x=0.0875 & y=0.0066.

I have tried some some formulas, but nothing is predicting with much accuracy.

Thanks for any help

J

Interpolation of measured data

Quote:

Originally Posted by **jhasting**

I have a measured data set (x & y are inputs, z is the result at those measures):

x y z

0.036802 0.004908 0.07158

0.036802 0.022135 0.10095

0.130886 0.004908 0.09627

0.130886 0.022135 0.12560

I would like a formula for interpolation, to predict z for all input conditions x & y (within bounds), for example when x=0.0875 & y=0.0066.

I have tried some some formulas, but nothing is predicting with much accuracy.

Thanks for any help

J

As always with problems of this type it would be helpfull to

know what process gives rise to the data, then we could fit

it with to an appropriate function.

However lacking such knowlege you could always try the

4-point interpolator given in Abramowitz and Stegun:

Suppose you know your functional value at points:

$\displaystyle (x_0,y_0),\ (x_0+h,y_0),\ (x_0,y_0+k),\ (x_0+h,y_0+k)$

then

$\displaystyle f(x_0+p.h,y_0+q.k)\ \approx \ (1-p).(1-q).f(x_0,y_0)\ +$

$\displaystyle p.(1-q).f(x_0+h,y_0)\ +$

$\displaystyle (1-p).q.f(x_0,y_0+k)\ +$

$\displaystyle p.q.f(x_0+h,y_0+k)$

Preferably with $\displaystyle 0 \leq p \leq 1 $ and $\displaystyle 0 \leq q \leq 1 $.