Math check needed

You can write this in matrix form much more elegantly.

Given

A = a_ij X = X(x) = x^i Y = Y(y) = y^j

then the interpolating function is

f(x,y) = X^T*A*Y

taking derivative w.r.t x or Y gives

f_x = X_x^T*A*Y f_y = X^T*A*Y_y

we can then compute the higher partials,

f_xx = X_xx^T*A*Y f_yy = X^T*A*Y_yy f_xy = X_x^T*A*Y_y

etc...

So these are your systems(you have yet to solve for A though)

Basically all you do is pre and post multiply A by x and its derivatives and y and its derivatives respectively to get the total derivative of f.

i.e.

Think of the formula as

f(x,y) = g(x)*C*h(y)

because that is essentially what you have

f_x = g'(x)*C*h(y) f_y = g(x)*C*h'(y)

etc...

Its just that one is dealing with matricies so you need to be careful with the order.

Note though that all the equations are of the form k = B^T*A*C. Each line represents an equation.

If you have some CAS package you should be able to compute the above matricies with ease and check your results.

Jon

a00=w0 a01=y0 a02=3*w2-3*w0-2*y0-y2 a03=2*w0-2*w2+y0+y2 a10=x0 a11=z0 a12=3*x2-3*x0-2*z0-z2 a13=2*x0-2*x2+z0+z2 a20=3*w1-3*w0-2*x0-x1 a21=3*y1-3*y0-2*z0-z1 a22=9*w0-9*w1-9*w2+9*w3+6*x0+3*x1-6*x2-3*x3+6*y0-6*y1+3*y2-3*y3+4*z0+2*z1+2*z2+z3 a23=6*w1-6*w0+6*w2-6*w3-4*x0-2*x1+4*x2+2*x3-3*y0+3*y1-3*y2+3*y3-2*z0-z1-2*z2-z3 a30=2*w0-2*w1+x0+x1 a31=2*y0-2*y1+z0+z1 a32=6*w1-6*w0+6*w2-6*w3-3*x0-3*x1+3*x2+3*x3-4*y0+4*y1-2*y2+2*y3-2*z0-2*z1-z2-z3 a33=4*w0-4*w1-4*w2+4*w3+2*x0+2*x1-2*x2-2*x3+2*y0-2*y1+2*y2-2*y3+z0+z1+z2+z3

Assuming you don't care to follow Jon's more basic derivation and you just want solutions to your equations, why not just put them into Scilab or Matlab or Mathcad? They're just linear equations (assuming that's a typo at y2 = ... +2Aa02 ...), and yield quickly to a matrix inversion.

I concur. Here's what I cut and pasted right out of Mathematica. It appears to be identical to what Klueless got.

a00=w0 a01=y0 a02=-3 w0+3 w2-2 y0-y2 a03=2 w0-2 w2+y0+y2 a10=x0 a11=z0 a12=-3 x0+3 x2-2 z0-z2 a13=2 x0-2 x2+z0+z2 a20=-3 w0+3 w1-2 x0-x1 a21=-3 y0+3 y1-2 z0-z1 a22=9 w0-9 w1-9 w2+9 w3+6 x0+3 x1-6 x2-3 x3+6 y0-6 y1+3 y2-3 y3+4 z0+2 z1+2 z2+z3 a23=-6 w0+6 w1+6 w2-6 w3-4 x0-2 x1+4 x2+2 x3-3 y0+3 y1-3 y2+3 y3-2 z0-z1-2 z2-z3 a30=2 w0-2 w1+x0+x1 a31=2 y0-2 y1+z0+z1 a32=-6 w0+6 w1+6 w2-6 w3-3 x0-3 x1+3 x2+3 x3-4 y0+4 y1-2 y2+2 y3-2 z0-2 z1-z2-z3 a33=4 w0-4 w1-4 w2+4 w3+2 x0+2 x1-2 x2-2 x3+2 y0-2 y1+2 y2-2 y3+z0+z1+z2+z3

"Don Lancaster" skrev i en meddelelse news: snipped-for-privacy@mid.individual.net...

There exists an ancient program called Maxima that does symbolic math. It works Ok to check the kiddies homework.