Hello /sci/, I am trying to find a general rule to calculate elements of an inverse matrix of a striped block diagonal matrix.
However, there doesnt seem to be much resources on the web about such matrices in total.
The best I could find was this article but it isnt quite what I am after:
https://doi.org/10.1016/j.cam.2005.02.012
There is also one grateful thing about my matrix - no mater how big it is, it always has a tridiagonal and a single element at the corners, like pic related.
However, this is not a Toeplitz matrix, as each element of the same color is not the same, the colors just denote the diagonals.
According to my current understanding, it shouldnt matter that the matrix is a block matrix, as inversion rules are the same, just numbers are replaced by blocks.
Perhaps someone here knows some appropriate resources? Is such a rule for this matrix even possible?
The article seems to hint that for certain matrices the inverse is banded or has some other non-full structure.
However, there doesnt seem to be much resources on the web about such matrices in total.
The best I could find was this article but it isnt quite what I am after:
https://doi.org/10.1016/j.cam.2005.02.012
There is also one grateful thing about my matrix - no mater how big it is, it always has a tridiagonal and a single element at the corners, like pic related.
However, this is not a Toeplitz matrix, as each element of the same color is not the same, the colors just denote the diagonals.
According to my current understanding, it shouldnt matter that the matrix is a block matrix, as inversion rules are the same, just numbers are replaced by blocks.
Perhaps someone here knows some appropriate resources? Is such a rule for this matrix even possible?
The article seems to hint that for certain matrices the inverse is banded or has some other non-full structure.
