We say that a symmetric matrix K is quasi-definite if it has the form K = [ −E AT A F ] where E and F are symmetric positive definite matrices. Although such matrices are indefinite, we show that any symmetric permutation of a quasi-definite matrix yields a factorization LDLT . We apply this result to obtain a new approach for solving the symmetric indefinite systems arising in interior-point m...

We discuss different cases of dissipative Hamiltonian differential-algebraic equations and the linear algebraic systems that arise in their linearization or discretization. For each case we give examples from practical applications. An important feature is (non-Hermitian) system matrix has a positive definite semidefinite Hermitian part. In can solve iteratively by Krylov subspace methods based...

In this paper, based on the shift splitting of coefficient matrix, a generalized two-sweep (GTSS) method is introduced to solve non-Hermitian positive definite linear systems. Theoretical analysis shows that GTSS convergent unique solution systems under loose restriction iteration parameter. Numerical experiments are reported efficiency method.

 ‎Using several examples of positive definite functions‎, ‎some inequalities for the numerical radius of‎ ‎matrices are investigated‎. ‎Also‎, ‎some open problems are stated‎.

Two-stage iterative methods for the solution of linear systems are studied. Convergence of both stationary and nonstationary cases is analyzed when the coefficient matrix is Hermitian positive definite. Keywords—Linear systems, Hermitian matrices, Positive definite matrices, Iterative methods, Nonstationary methods, Two-stage methods.