Combination of real and imaginary parts (CRI) works well for solving complex symmetric linear systems. This paper develops a generalization CRI method to determine the solution Sylvester matrix equation. We show that this, regardless condition, converges At end we test new scheme by numerical example.

The matrix equation X + ATX−1A = Q has been studied extensively when A and Q are real square matrices and Q is symmetric positive definite. The equation has positive definite solutions under suitable conditions, and in that case the solution of interest is the maximal positive definite solution. The same matrix equation plays an important role in Green’s function calculations in nano research, ...

In the present paper, among other results, a decomposition formula is given for the w-bounded continuous negative definite functions of a topological *-semigroup S with a weight function w into a proper H*-algebra A in terms of w-bounded continuous positive definite A-valued functions on S. A generalization of a well-known result of K. Harzallah is obtained. An earlier conjecture of the author ...

Several Riemannian metrics and families of were defined on the manifold Symmetric Positive Definite (SPD) matrices. Firstly, we formalize a common general process to define metrics: principle deformed metrics. We relate recently introduced family alpha-Procrustes class mean kernel by providing sufficient condition under which elements former belong latter. Secondly, focus balanced bilinear form...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 29 January 2021Accepted: 19 July 2021Published online: 11 November 2021Keywordsrandomized methods, Nyström's method, low rank, preconditioner, symmetric positive definite, Schur complementAMS Subject Headings65F08, 65F50, 65F55Publication DataISSN (print): 1064-8275ISSN (...