The inverse of banded matrices
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The inverses of r-banded matrices, for r = 1,2,3 have been thoroughly investigated as one can see from the references we provide. Let Br,n (1<r<n) be and n X n matrix of entries (aij), -r<i<r, 1<j<r, with the remaining un-indexed exries all zeros. In this paper, generalizing a method of Mallik (199) (5), we give the LU factorization and the inverse of the matrix Br,n (if it exists). Our results are valid for an arbitrary square matrix (taking r = n), and so, we will give a new approach for cocmparing the inverse of an invertible square matrix. Our method is based on Hessenberg submatrices associated to Br,n.
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