As my numerics professor said, "The more dimensions, the more you curse" :) This has to do with trying to get a finer estimate of a problem. Suppose you have

As my numerics professor said, "The more dimensions, the more you curse" :) This has to do with trying to get a finer estimate of a problem. Suppose you have a one dimensional problem you're trying to solve. You take the line segment, break it into 100 pieces. These techniques usually a matrix with about 100 rows in it, and you have to invert it / find and eigenvalue, etc. These are O(n^2) or O(n^3) depending on the problem. Now, let's get a better estimate, and use 200 points. We've doubled the number of points, so our solution now takes 4 to 8 times longer, depending on the type of problem. Switch gears to a 2d problem. You now have a 100 X 100 mesh, that creates a matrix with 10,000 elements. If you want to improve the accuracy, you need a 200 X 200 mesh, which creates a 40,000 element matrix. Our algorithms cost O(n^4) and O(n^6) to get a better measurement now. Now consider 3 dimensions and beyond. Your 100 x 100 x 100 system becomes a 200 x 200 x 200 system. This makes what is technically known a FREAKING HUGE matrix. Your algorithm is effectively O(n^6) or O(n^9), depending on the problem type. You can see how this gets nasty quickly. HTH