Solving an equation through optimization..........

2013 2 25
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Y=Ax
y is a mX1 matrix
A is a mXn matrix
x is a nX1 matrix
AA'=I
Here we apply optimization technique to solve x instead of taking inverse of A. Will you explain me why...............Please help me........

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Walter Roberson
Walter Roberson 2013-2-25

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inverse is only strictly defined for square matrices.
You could use pinv() or the backslash operator ('\')

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Tinkul
Tinkul 2013-2-25
A is a square matrix.Even though A is a square matrix we apply optimization...Why.....
Walter Roberson
Walter Roberson 2013-2-25
No, you said A is mxn which is not square unless m == n
Tinkul
Tinkul 2013-2-25
Sorry,i applogy for that...m==n(ie, A is square matrix).Then why we use optimization...
Tinkul
Tinkul 2013-2-25
Sir, will you tell me why optimization algorithm is used to solve Y=Ax instead of taking A inverse.
Walter Roberson
Walter Roberson 2013-2-25
http://blogs.mathworks.com/loren/2007/05/16/purpose-of-inv/#2
There are good reasons to not use inv however. The main one is
numerical considerations.
Here is the second paragraph of the description for inv in the documentation:
In practice, it is seldom necessary to form the explicit inverse of a matrix. A frequent misuse of inv arises when solving the system of linear equations.
One way to solve this is with x = inv(A)*b. A better way, from both an execution time and numerical accuracy standpoint, is to use the matrix division operator x = A\b. This produces the solution using Gaussian elimination, without forming the inverse. See \ and / for further information.
Walter Roberson
Walter Roberson 2013-2-25
So EXECUTION TIME and NUMERICAL ACCURACY.

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