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...

with A a diagonal matrix. Appropriate boundary and initial conditions are given. The amplification matrix Q(£) need not be diagonal. However, he required that |Q(£)| ^ 1We use certain results in matrix theory and Wiener-Hopf factorization to replace this restrictive assumption by certain reasonable assumptions on accuracy of Q(£) and smoothness of an associated positive-definite symmetric matri...

Based on a particular node ordering and corresponding block decomposition of the matrix we analyse an e cient, algebraic multilevel preconditioner for the iterative solution of nite element discretizations of elliptic boundary value problems. Thereby an analysis of a new version of block-factorization preconditioning methods is presented. The approximate factorization requires an approximation ...

Item recommendation from implicit, positive only feedback is an emerging setup in collaborative filtering in which only one class examples are observed. In this paper, we propose a novel method, called User Graph regularized Pairwise Matrix Factorization (UGPMF), to seamlessly integrate user information into pairwise matrix factorization procedure. Due to the use of the available information on...