Gaussian pivoting method for solving linear complementarity problem (Q1377180)

Direct methods for solving linear complementarity problems are considered. A new direct method using Gaussian pivoting steps is proposed. The method is suitable for a coefficient matrix not only to be an \(M\)-matrix but also to be a general \(Z\)-matrix. The computational complexity of the method is polynomial at most \({1\over 3} n^3+ O(n^2)\). When the coefficient matrix is a \(Z\)-matrix, the complexity can be reduced to \({1\over 6} n^3+ O(n^2)\) for a symmetric \(Z\)-matrix and to \(O(n)\) for a tridiagonal \(Z\)-matrix.