# How to apply a function independently for a set of data?

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Benson Gou on 4 Jun 2021
Commented: Walter Roberson on 5 Jun 2021
Dear All,
I have a set of data {Ai, bi}, i = 1, ..., N. I want to apply a function which solves Ai(xi) = bi, a nonliear problem. {Ai, bi} is indepentent and has nothing to do with each other for all i. My question is how to apply the function to solve the group together, A = [A1 A2 ... AN], b = [b1, b2, ..., bN]. My goal is to speed up my computation.
The original process is that I repeatly run the function N times to solve Ai(xi)=bi, i = 1, ..., N, where xi is a single variable. Now I want to run the function at one time to solve all Ai(xi)=bi, i=1,...,N, together. My rough idea is to form a matrix A = [A1 A2 ... AN], b = [b1 b2 ... bN], and then run the fucntion one time to solve all xi, i = 1, ..., N. But I am wondering if there is a simpler way to solve all equations together.
Thanks a lot.
Benson
Walter Roberson on 5 Jun 2021
Whether your approach would work or not would depend upon the computation involved. In some cases it might be quite efficient to do all of the matrices at the same time; in other cases it might be mathematically difficult to do all of them at the same time. Or it just might not be efficient to solve them all at the same time.
We would need to know more about the computation to advise further.

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