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The inverse of a banded matrix 
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#1
Jun1214, 05:52 PM

P: 601

Hello all,
I have say 512by512 matrix, but based on the structure of this matrix most elements not on the diagonals between 5 to +5 ( stand for diagonal below the main diagonal, and + for diagonal above the main diagonal) are small relative to the elements of the mentioned diagonals. So, I create a 512by512 banded matrix, where I null all other elements not on the mentioned diagonals. Now the question is: will there be a huge complexity saving if I want the inverse of the matrix by inverting its banded version instead of the original matrix? Thanks 


#2
Jun1214, 07:12 PM

Engineering
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Thanks
P: 7,177

In computer calculations, "inverting a matrix" is almost always the wrong thing to do, even if you have a nice looking math equation with an inverse matrix in it.
In this case there will be a huge "complexity" increase, because the inverse matrix will be fully populated, not banded. What you really want to do is probably solve a set of equations or something similar. If you decompose your banded matrix as A = LDU or something similar, where L and U are lower and upper triangular and have the same bandwidth as A, you preserve the efficiency by not needing to process all the zero terms in L and U. 


#3
Jun2114, 04:01 PM

P: 601




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