Abstract. In this paper some results are reviewed concerning the characterization of inverses of symmetric tridiagonal and block tridiagonal matrices as well as results concerning the decay of the elements of the inverses. These results are obtained by relating the elements of inverses to elements of the Cholesky decompositions of these matrices. This gives explicit formulas for the elements of the inverse and gives rise to stable algorithms to compute them. These expressions also lead to bounds for the decay of the elements of the inverse for problems arising from discretization schemes. Basically there are two kinds of papers: the first gives analytic formulas for special cases; the second gives characterizations of matrices whose inverse has certain properties, e.g., being tridiagonal or banded. Historically, the oldest paper we found considering the explicit inverse of matrices
Meurant REF reviewed the connections between the inverse of a block tridiagonal matrix and its twisted factorization, thereby deducing formulas for the blocks of the inverse of a block tridiagonal matrix.
A Review on the Inverse of Symmetric Tridiagonal and Block Tridiagonal Matrices
SIAM J. Matrix Analysis Applications
SIAM J. Matrix Analysis Applications
Computer Science Mathematics