On the Effective Computation of the Inertia of a Non-Hermitian Matrix.
On the efficient update of rectangular LU-factorizations subject to low rank modifications.
On the Eigenproblem for Normal Matrices.
On the Eigenvalue Distribution of a Class of Preconditioning Methods.
On the equivalence of primal and dual substructuring preconditioners.
On the Fast Matrix Multiplication in the Boundary Element Method by Panel Clustering.
On the fast reduction of symmetric rationally generated Toeplitz matrices to tridiagonal form.
On the generalized Riccati matrix differential equation. Exact, approximate solutions and error estimate
In this paper explicit expressions for solutions of Cauchy problems and two-point boundary value problems concerned with the generalized Riccati matrix differential equation are given. These explicit expressions are computable in terms of the data and solutions of certain algebraic Riccati equations related to the problem. The interplay between the algebraic and the differential problems is used in order to obtain approximate solutions of the differential problem in terms of those of the algebraic...
On the global and cubic convergence of a quasi-cyclic Jacobi method.
On the Global Convergence of the Eberlein Method for Real Matrices.
On the Invariance of Perturbed Null Vectors Under Column Scaling.
On the inverse eigenvalue problem for a special kind of acyclic matrices
We study an inverse eigenvalue problem (IEP) of reconstructing a special kind of symmetric acyclic matrices whose graph is a generalized star graph. The problem involves the reconstruction of a matrix by the minimum and maximum eigenvalues of each of its leading principal submatrices. To solve the problem, we use the recurrence relation of characteristic polynomials among leading principal minors. The necessary and sufficient conditions for the solvability of the problem are derived. Finally, a...
On the local convergence of Kung-Traub's two-point method and its dynamics
In this paper, the local convergence analysis of the family of Kung-Traub's two-point method and the convergence ball for this family are obtained and the dynamical behavior on quadratic and cubic polynomials of the resulting family is studied. We use complex dynamic tools to analyze their stability and show that the region of stable members of this family is vast. Numerical examples are also presented in this study. This method is compared with several widely used solution methods by solving test...
On the LU Factorization of M-Matrices.
On the Monotonity of Incomplete Factorization.
On the Multigrid Solution of Finite Element Equations With Isoparametric Elements.
On the Multi-Level Splitting of Finite Element Squares.
On the Numerical Errors in One Step Algorithms for Time Dependent Problems.
On the parallel solution of tridiagonal systems by wrap-around partitioning and incomplete LU factorization.
On the parameter in augmented Lagrangian preconditioning for isogeometric discretizations of the Navier-Stokes equations
In this paper, we deal with the optimal choice of the parameter for augmented Lagrangian preconditioning of GMRES method for efficient solution of linear systems obtained from discretization of the incompressible Navier-Stokes equations. We consider discretization of the equations using the B-spline based isogeometric analysis approach. We are interested in the dependence of the convergence on the parameter for various problem parameters (Reynolds number, mesh refinement) and especially for...