Solving the following equation without taking inverse.

How to solve the following equation for calculating the D:

D=|inv(B)|∗|g|

here, B is a non-singular square matrix and g is a column vector of the length equal to the no of elements in the row of B. Modules is applied element-wise.

The solution of this without taking the inverse.

[KHAN WALI]

and I reach this point now)) if you have found the solution please share, did you use LU factorization? singular value decomposition etc? or what ever method you used, please share

[Matt J]

In what application does the need for this arise?

[KHAN WALI]

In my case B is singular matrix.

[Walter Roberson]

@KHAN WALI

If it were not for the part of the then with singular matrices you would typically switch to using

What is the mathematical situation that leads you to want to have the part? And would using

D = abs(pinv(B)) * abs(g)

be acceptable for your situation?

[Torsten]

I also didn't read the title of the contribution and thought:

Why not simply

D = abs(inv(B))*abs(g)

?

Answer 1

[Chunru]

In matlab, you can solve the linear system by mldivide or \

"doc mldivide" for detailed description.

B= randn(4, 4)

B = 4×4

-0.0294 0.1957 -1.5414 -0.1266 0.2383 0.9828 0.2350 -0.1879 -0.2651 -0.7456 1.1097 0.4562 -0.7198 -0.0695 -0.1106 0.3846

g = randn(4, 1)

g = 4×1

0.3455 -0.6763 -2.1197 -1.6276

f = B \ g

f = 4×1

-3.8263 -2.1101 0.5352 -11.6193

B * f

ans = 4×1

0.3455 -0.6763 -2.1197 -1.6276

[Walter Roberson]

Notice in the original question,

Modules is applied element-wise

That is, the we see is absolute value of each element of g, and the is absolute value of each element of the inverse of B.

It is easy enough in your code to use B\abs(g) so there is no concern about the part. But the MATLAB \ operator does not take absolute value of the inverse, and there is no option to force it to.

This feels like a constrained least squares. I wonder if https://www.mathworks.com/help/matlab/ref/lsqnonneg.html can be used?