An Asymptotic Approach for Testing P0-Matrices

A direct approach to the P-matrix or P0-matrix problem is to evaluate all the principal minors of matrix A using standard numerical linear algebra techniques with O(n2n3) computational time complexity. The computational time complexity of the P-matrix problem has been reduced from O(n2n3) to O(n2) by applying recursively a criterion for P-matrices based on Schur complementation. But this algorithm can be not directly applied to test the P0-matrices because the Schur complementation can be not computed when some zero diagonal elements appear.This paper proposes an asymptotic approach for testing P0-matrices with O(n2) computational time complexity. Some numerical examples show that the proposed algorithm is effective for testing P0-matrices.