An Implementation of the Method of Ermakov and Zolotukhin for Multidimensional Integration and Interpolation.
An Implementation of Vincent's Theorem.
An implicit approximate inverse preconditioner for saddle point problems.
An implicit iteration method for variational inequalities over the set of common fixed points for a finite family of nonexpansive mappings in Hilbert spaces.
An implicit method for fuzzy parabolic partial differential equations.
An implicit restarted Lanczos method for large symmetric eigenvalue problems.
An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations
In this article, we consider the initial value problem which is obtained after a space discretization (with space step ) of the equations governing the solidification process of a multicomponent alloy. We propose a numerical scheme to solve numerically this initial value problem. We prove an error estimate which is not affected by the step size chosen in the space discretization. Consequently, our scheme provides global convergence without any stability condition between and the time step size...
An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations
In this article, we consider the initial value problem which is obtained after a space discretization (with space step h) of the equations governing the solidification process of a multicomponent alloy. We propose a numerical scheme to solve numerically this initial value problem. We prove an error estimate which is not affected by the step size h chosen in the space discretization. Consequently, our scheme provides global convergence without any stability condition between h and the time...
An Improved Calculation of the General Elliptic Integral of the Second Kind in the Neighbourhood of x= 0.
An improved convergence analysis of a superquadratic method for solving generalized equations.
An improved convergence analysis of Newton's method for twice Fréchet differentiable operators
We develop local and semilocal convergence results for Newton's method in order to solve nonlinear equations in a Banach space setting. The results compare favorably to earlier ones utilizing Lipschitz conditions on the second Fréchet derivative of the operators involved. Numerical examples where our new convergence conditions are satisfied but earlier convergence conditions are not satisfied are also reported.
An improved upper bound for the discrepancy of quadratic congruential pseudorandom numbers
An improvement of Euclid's algorithm
The paper introduces the calculation of a greatest common divisor of two univariate polynomials. Euclid’s algorithm can be easily simulated by the reduction of the Sylvester matrix to an upper triangular form. This is performed by using - transformation and -factorization methods. Both procedures are described and numerically compared. Computations are performed in the floating point environment.
An incomplete-factorization preconditioning using repeated red-black ordering.
An infinite dimensional analogue of R. S. Varga's lemma
An Ingham type proof for a two-grid observability theorem
Here, we prove the uniform observability of a two-grid method for the semi-discretization of the -wave equation for a time ; this time, if the observation is made in , is optimal and this result improves an earlier work of Negreanu and Zuazua [C. R. Acad. Sci. Paris Sér. I 338 (2004) 413–418]. Our proof follows an Ingham type approach.
An Ingham type proof for a two-grid observability theorem
Here, we prove the uniform observability of a two-grid method for the semi-discretization of the 1D-wave equation for a time ; this time, if the observation is made in , is optimal and this result improves an earlier work of Negreanu and Zuazua [C. R. Acad. Sci. Paris Sér. I338 (2004) 413–418]. Our proof follows an Ingham type approach.
An instantaneous semi-Lagrangian approach for boundary control of a melting problem
In this paper, a sub-optimal boundary control strategy for a free boundary problem is investigated. The model is described by a non-smooth convection-diffusion equation. The control problem is addressed by an instantaneous strategy based on the characteristics method. The resulting time independent control problems are formulated as function space optimization problems with complementarity constraints. At each time step, the existence of an optimal solution is proved and first-order optimality conditions...
An Integral Equation Method for the Numerical Conformal Mapping of Interior, Exterior and Doubly-Connected Domains
An integral inequality for convex functions and applications in numerical integration.