Need help

[Cortana]

So here's the question:

I have a dataset of one-dimensional vectors, each of those has a corresponding N-dimensional vector. The task is: given a one-dimensional vector from outside the dataset, predict the corresponding N-dimensional vector.
In other words, I somehow need to learn a function f(x)->(y1, y2,..., yN) or f(x)->([a1,b1], [a2,b2],..., [aN,bN]), where y1 belongs to [a1,b1] and so on (a and b as close together as possible).
Would really appreciate any suggestions, I'm kinda stuck - the methods I've tried didn't perform well.

[Cortana]

To AvDav and ByTheWay:
Thanks guys, I appreciate the humor

To Intel and W_z_rd:
The thing is that my original problem was finding a function that
would map 9-dimensional data to 1-dimensional (the opposite of the
current one). So naturally I looked at it as the same problem with
different dimensionality. It didn't really occur to me to look at it
this way. So thanks for opening my eyes
Anyways, my dataponts are scattered all over the place and don't seem
to belong to any more or less simple line. But I thought I might as
well try it. I tried polynomial and FFT-based interpolations and my
favorite neural networks. None of them really work. So if you have any
other methods in mind I'll be happy to try them out
I guess for now I'll just get splines working and see how it goes.

[Junior]

Cortana, can you describe your problem, precisely? What is your data? What is your input, what is your output? Some normal example? Tell what is "close", an Euclydean distance, a Manhattan distance, something else? What is your dataset, a table in database, or just a data structure in RAM? Can we, for example, suggest you some data mining?
You see, you assume we know what all is about, but we don't. Take some time to describe everything from scratch, and we will take some time to think about it with you!