Re: ? best approx of matrix of a linear sys

In article <ffLfg.11715$Qg.8715@xxxxxxxxxxxxxxxxxxxxxxxx>,
"Cheng Cosine" <acosine@xxxxxxxxxxxx> wrote:

Hi:

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?

Thanks,
by Cheng Cosine
Jun/01/2k6 NC

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.
.

Relevant Pages

  • Re: ? best approx of matrix of a linear sys
    ... 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 ... The matrix A is unknown. ...
    (sci.math)
  • Re: ? best approx of matrix of a linear sys
    ... If one has a matrix, rather that a linear function, then one has the ... The matrix A can be determined by by its effects on the column matrix ... vectors, the x's, with a single entry of 1 and other entries zero. ...
    (sci.math)