An algorithm for symmetric indefinite linear systems (Q2917719)

The authors consider an algorithm for solving a symmetric indefinite system \(Ax=b\). The preprocessing, based on the weighted matchings, is proposed to the original system to gain a new (symmetric indefinite) linear system \(\hat A \hat x= \hat b\). The main goal of this paper is to present the so-called boundedly partial pivoting in the incomplete \(LDL^{\text{T}}\) factorization of \(\hat A\) with an error \(E\): \(M:=LDL^{\text{T}}=\hat A-E\). It is backward stable due to boundedness of the lower triangular factor \(L\). Moreover, in this pivoting besides concerning the tridiagonal pivoting algorithm there exist no permutations of rows and columns. Lastly, the solution of \(M^{-1}\hat A \hat x=M^{-1} \hat b\) is obtained in terms of the SQMR iterative method.