I am working on a sample data interpolation project {(x_i,y_i)}where the input domain for x_iis in 4D space and the output y_iis in three-dimensional space. I need to create two lookup tables for both directions. I managed to create a table 4D -> 3D. But 3D -> 4Done is complicated. Sample data is not at regular grid points, and this is not a single display. Is there any known treatment for this situation? I did a search on the Internet, but what I found applies only to displays 3D -> 3Dthat are not suitable for this case. Thank!
To answer Spect questions:
X(3D) -> Y(4D) occurs 1X -> nY
I want to create a table that for any given X, we can find the value for Y. Sample data does not occupy the entire area X. But this is good, we only need accuracy for the point inside the sample data area. For example, we have example data, for example {(x1,x2,x3) ->(y1,y2,y3,y4)}. Perhaps we also have sample data {(x1,x2,x3) -> (y1_1,y2_1,y3_1,y4_1)}. But everything is in order. We need a table for anyone (a,b,c)in space X; it corresponds to ONE (e,f,g,h)in space Y. There may be more than one choice, but we need only one. (Sorry for the invalid character)
One possible way to handle this: since I already set the smooth display from Y->X, I can use the Newton method or any other method to reverse search for a point Yfor any given one X. But this is not accurate enough and time consuming. Since I need to search for each point in the table, and the error is the sum of the model error with the search error.
So, I want to know that you can find a match directly to interpolate the sampled data instead of doing such a search in 3.