Re: ? best approx of matrix of a linear sys


"Virgil" <vmhjr2@xxxxxxxxxxx> wrote in message
news:vmhjr2-3EAD97.21575401062006@xxxxxxxxxxxxxxxxxxxxxxxxx
In article <ffLfg.11715$Qg.8715@xxxxxxxxxxxxxxxxxxxxxxxx>,
"Cheng Cosine" <acosine@xxxxxxxxxxxx> wrote:


Suppose one has a black box of linear system: A*x = b, for any given
vector
x the corresponding vector b

can be determined. It is called a black box because entries of matrix A
are
unknown and are to be determined.

A straightforward approach is to have a set of linearly independent
vectors
x and b so that one has:

A*X = B => A = B*inv(B), where A is M-by-N and, X is N-by-N, and B is
M-by-M.

But this approach requires significant computer memory and cannot be
performed. Are there more "economic"

approach to determine A or to determine some best approximation of A?

...
If one has a matrix, rather that a linear function, then one has the
standard basis of column matrix vectors with a single entry of 1 and
other entries zero, and each column of A is A times one of these basis
vectors.

Don't get your point. The matrix A is unknown.

by Cheng Cosine
Jun/03/2k6 NC




.

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