An extended block Arnoldi algorithm for large-scale solutions of the continuous-time algebraic Riccati equation.
An Extension of 3D Zernike Moments for Shape Description and Retrieval of Maps Defined in Rectangular Solids
Zernike polynomials have been widely used in the description and shape retrieval of 3D objects. These orthonormal polynomials allow for efficient description and reconstruction of objects that can be scaled to fit within the unit ball. However, maps defined within box-shaped regions ¶ for example, rectangular prisms or cubes ¶ are not well suited to representation by Zernike polynomials, because these functions are not orthogonal over such regions. In particular, the representations require many...
An extension of A. Ostrowski's Theorem on the round-off stability of iterations.
An extension of Rothe's method to non-cylindrical domains
In this paper Rothe’s classical method is extended so that it can be used to solve some linear parabolic boundary value problems in non-cylindrical domains. The corresponding existence and uniqueness theorems are proved and some further results and generalizations are discussed and applied.
An Extension of the ...2 Procedure.
An extension of the auxiliary problem principle to nonsymmetric auxiliary operators
An Extension of the Auxiliary Problem Principle to Nonsymmetric Auxiliary Operators
To find a zero of a maximal monotone operator, an extension of the Auxiliary Problem Principle to nonsymmetric auxiliary operators is proposed. The main convergence result supposes a relationship between the main operator and the nonsymmetric component of the auxiliary operator. When applied to the particular case of convex-concave functions, this result implies the convergence of the parallel version of the Arrow-Hurwicz algorithm under the assumptions of Lipschitz and partial Dunn properties...
An Extension of the Lax-Richtmyer Theory.
An extension of the perturbation analysis for the Drazin inverse.
An extension of the root perturbation -dimensional polynomial factorization method
An Extrapolation Method for the Quadrature of Functions with Singularities in the Vicinity of the Interval of Integration.
An Extrapolation Method with Step Size Control for Nonlinear Volterra Integral Equations.
An -Galerkin method for a Stefan problem with a quasilinear parabolic equation in nondivergence form.
An hp-Discontinuous Galerkin Method for the Optimal Control Problem of Laser Surface Hardening of Steel
In this paper, we discuss an hp-discontinuous Galerkin finite element method (hp-DGFEM) for the laser surface hardening of steel, which is a constrained optimal control problem governed by a system of differential equations, consisting of an ordinary differential equation for austenite formation and a semi-linear parabolic differential equation for temperature evolution. The space discretization of the state variable is done using an hp-DGFEM, time and control discretizations are based on a discontinuous Galerkin...
An hp-Discontinuous Galerkin Method for the Optimal Control Problem of Laser Surface Hardening of Steel
In this paper, we discuss an hp-discontinuous Galerkin finite element method (hp-DGFEM) for the laser surface hardening of steel, which is a constrained optimal control problem governed by a system of differential equations, consisting of an ordinary differential equation for austenite formation and a semi-linear parabolic differential equation for temperature evolution. The space discretization of the state variable is done using an hp-DGFEM, time and control discretizations are based on a discontinuous Galerkin...
An IMEX scheme for reaction-diffusion equations: application for a PEM fuel cell model
An implicit-explicit (IMEX) method is developed for the numerical solution of reaction-diffusion equations with pure Neumann boundary conditions. The corresponding method of lines scheme with finite differences is analyzed: explicit conditions are given for its convergence in the ‖·‖∞ norm. The results are applied to a model for determining the overpotential in a proton exchange membrane (PEM) fuel cell.
An immediate analysis for global superconvergence for integrodifferential equations
In this paper we study the finite element approximations to the parabolic and hyperbolic integrodifferential equations and present an immediate analysis for global superconvergence for these problems, without using the Ritz projection or its modified forms.
An imperfect conjugate gradient algorithm
A new biorthogonalization algorithm is defined which does not depend on the step-size used. The algorithm is suggested so as to minimize the total error after steps if imperfect steps are used. The majority of conjugate gradient algorithms are sensitive to the exactness of the line searches and this phenomenon may destroy the global efficiency of these algorithms.
An Implementation of Ray Tracing Algorithm for the Multiprocessor Machines
An implementation of recursive quadratic programming variable metric methods for linearly constrained nonlinear minimax approximation