A Constructive Method for Deriving Finite Elements of Nodal Type.
A Constructive Method of Solving the Liapounov Equation for Complex Matrices.
A continuous finite element method with face penalty to approximate Friedrichs' systems
A continuous finite element method to approximate Friedrichs' systems is proposed and analyzed. Stability is achieved by penalizing the jumps across mesh interfaces of the normal derivative of some components of the discrete solution. The convergence analysis leads to optimal convergence rates in the graph norm and suboptimal of order ½ convergence rates in the L2-norm. A variant of the method specialized to Friedrichs' systems associated with elliptic PDE's in mixed form and reducing the number...
A Continuous Selection of the Metric Projection in Matrix Spaces, Addendum.
A Contour Integral Representation of Linear Extrapolation Methods.
A contribution to Balas' algorithm
A contribution to Collatz's eigenvalue inclusion theorem for nonnegative irreducible matrices.
A contribution to Runge-Kutta formulas of the 7th order with rational coefficients for systems of differential equations of the first order
The purpose of this article is to find the 7th order formulas with rational parameters. The formulas are of the 11th stage. If we compare the coefficients of the development up to with the development given by successive insertion into the formula for and we obtain a system of 59 condition equations with 65 unknowns (except, the 1st one, all equations are nonlinear). As the solution of this system we get the parameters of the 7th order Runge-Kutta formulas as rational numbers.
A contribution to solving a system of two non-linear equations
A contribution to solving a system of two non-linear equations
A contribution to the successive over-relaxation method
A Contribution to the Theory of Condition.
A Convergence Analysis of Hopscotch Methods for Fourth Order Parabolic Equations.
A convergence analysis of Newton-like methods for singular equations using outer or generalized inverses
The Newton-Kantorovich approach and the majorant principle are used to provide new local and semilocal convergence results for Newton-like methods using outer or generalized inverses in a Banach space setting. Using the same conditions as before, we provide more precise information on the location of the solution and on the error bounds on the distances involved. Moreover since our Newton-Kantorovich-type hypothesis is weaker than before, we can cover cases where the original Newton-Kantorovich...
A convergence analysis of Newton's method under the gamma-condition in Banach spaces
We provide a local as well as a semilocal convergence analysis for Newton's method to approximate a locally unique solution of an equation in a Banach space setting. Using a combination of center-gamma with a gamma-condition, we obtain an upper bound on the inverses of the operators involved which can be more precise than those given in the elegant works by Smale, Wang, and Zhao and Wang. This observation leads (under the same or less computational cost) to a convergence analysis with the following...
A convergence analysis of SOR iterative methods for linear systems with weakH-matrices
It is well known that SOR iterative methods are convergent for linear systems, whose coefficient matrices are strictly or irreducibly diagonally dominant matrices and strong H-matrices (whose comparison matrices are nonsingular M-matrices). However, the same can not be true in case of those iterative methods for linear systems with weak H-matrices (whose comparison matrices are singular M-matrices). This paper proposes some necessary and sufficient conditions such that SOR iterative methods are...
A Convergence Condition for the Quadrilateral Wilson Element.
A convergence proof of a special version of the generalized reduced gradient method (GRGS)
A convergence result and numerical study for a nonlinear piezoelectric material in a frictional contact process with a conductive foundation
We consider two static problems which describe the contact between a piezoelectric body and an obstacle, the so-called foundation. The constitutive relation of the material is assumed to be electro-elastic and involves the nonlinear elastic constitutive Hencky's law. In the first problem, the contact is assumed to be frictionless, and the foundation is nonconductive, while in the second it is supposed to be frictional, and the foundation is electrically conductive. The contact is modeled with the...
A convergence result for an iterative method for the equations of a stationary quasi-newtonian flow with temperature dependent viscosity