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I am trying to solve a large system of linear equations. The form of the matrix is A = T + F. T is basically a tridiagonal matrix and F has two "lines" of numbers running parallel to the diagonal but at some distance. Basically like this one, but not symmetric, nor is it diagonally dominant.

Questions:

Is there any efficient algorithm to solve this kind of matrix?

Is there any way to turn the matrix into a diagonally dominant one, so that a straight forward iterative method could be used?

Could one make a custom iterative method, that does not require diagonal dominance? Would [itex]\overline{x}_{i+1} = T^{-1}(\overline{b}-F \overline{x}_{i}) [/itex] work?

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# Tridiagonal matrix with fringes

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