Schur complement-based infinity norm bounds for the inverse of $ S $-Sparse Ostrowski Brauer matrices

In this paper, we study the Schur complement problem of $ S $-SOB matrices, and prove that the Schur complement of $ S $-Sparse Ostrowski-Brauer ($ S $-SOB) matrices is still in the same class under certain conditions. Based on the Schur complement of $ S $-SOB matrices, some upper bound for the infinite norm of $ S $-SOB matrices is obtained. Numerical examples are given to certify the validity of the obtained results. By using the infinity norm bound, an error bound is given for the linear complementarity problems of $ S $-SOB matrices.