In this paper, an iterative method is proposed for solving the matrix inverse problem AX = B for Hermitian-generalized Hamiltonian matrices with a submatrix constraint. By this iterative method, for any initial matrix A0, a solution A ∗ can be obtained in finite iteration steps in the absence of roundoff errors, and the solution with least norm can be obtained by choosing a special kind of init...

We describe a new extension to ScaLAPACK [2] for computing with symmetric (Hermi-tian) matrices stored in a packed form. The new code is built upon the ScaLAPACK routines for full dense storage for a high degree of software reuse. The original ScaLAPACK stores a symmetric matrix as a full matrix but accesses only the lower or upper triangular part. The new code enables more efficient use of mem...

A new form of the Kerr solution is presented. The solution involves a time coordinate which represents the local proper time for free-falling observers on a set of simple trajectories. Many physical phenomena are particularly clear when related to this time coordinate. The chosen coordinates also ensure that the solution is well behaved at the horizon. The solution is well suited to the tetrad ...

In this paper we define a new type of rings ”almost powerhermitian rings” (a generalization of almost hermitian rings) and establish several sufficient conditions over a ring R such that, every regular matrix admits a diagonal power-reduction.

The positive definite solutions of the nonlinear matrix equation Xs + A∗f(X)A = Q are discussed. A necessary and sufficient condition for the existence of positive definite solutions for this equation is derived.Then, the uniqueness of the Hermitian positive definite solution is studied based on an iterative method proposed in this paper. Lastly the perturbation analysis for this equation is di...

Let A − λB and C − λD be two normal matrix pencils or Hermitian matrix pencils or definite matrix pencils, and let AXD −BXC = S. Our main results in this part are estimates of a unitarily invariant norm of the solution X under some conditions on the spectra of two pencils. §

Non-stationary multisplitting algorithms for the solution of linear systems are studied. Convergence of these algorithms is analyzed when the coefficient matrix of the linear system is hermitian positive definite. Asynchronous versions of these algorithms are considered and their convergence investigated.

We consider real-valued preconditioned Krylov subspace methods for the solution of complex linear systems, with an emphasis on symmetric (non-Hermitian) problems. Different choices of the real equivalent formulation are discussed, as well as different types of block preconditioners for Krylov subspace methods. Numerical experiments illustrating the performance of the various approaches are pres...

This paper discusses the large N limit of the two-Hermitian-matrix model in zero dimensions, using the hidden BRST method. A system of integral equations previously found is solved, showing that it contained the exact solution of the model in leading order of large N . ∗Permanent address: Fac. de Fisica, Universidad Católica de Chile, Casilla 306, Santiago 22, Chile.