Quantitative Estimates for the Finite Section Method
نویسندگان
چکیده
The finite section method is a classical scheme to approximate the solution of an infinite system of linear equations. We present quantitative estimates for the rate of the convergence of the finite section method on weighted `-spaces. Our approach uses recent results from the theory of Banach algebras of matrices with off-diagonal decay. Furthermore, we demonstrate that Banach algebra theory provides a natural framework for deriving a finite section method that is applicable to large classes of non-hermitian matrices. An example from digital communication illustrates the practical usefulness of the proposed theoretical framework.
منابع مشابه
A posteriori $ L^2(L^2)$-error estimates with the new version of streamline diffusion method for the wave equation
In this article, we study the new streamline diffusion finite element for treating the linear second order hyperbolic initial-boundary value problem. We prove a posteriori $ L^2(L^2)$ and error estimates for this method under minimal regularity hypothesis. Test problem of an application of the wave equation in the laser is presented to verify the efficiency and accuracy of the method.
متن کاملOptimal order finite element approximation for a hyperbolic integro-differential equation
Semidiscrete finite element approximation of a hyperbolic type integro-differential equation is studied. The model problem is treated as the wave equation which is perturbed with a memory term. Stability estimates are obtained for a slightly more general problem. These, based on energy method, are used to prove optimal order a priori error estimates.
متن کاملA new positive definite semi-discrete mixed finite element solution for parabolic equations
In this paper, a positive definite semi-discrete mixed finite element method was presented for two-dimensional parabolic equations. In the new positive definite systems, the gradient equation and flux equations were separated from their scalar unknown equations. Also, the existence and uniqueness of the semi-discrete mixed finite element solutions were proven. Error estimates were also obtaine...
متن کاملPrediction of Human Vertebral Compressive Strength Using Quantitative Computed Tomography Based Nonlinear Finite Element Method
Introduction: Because of the importance of vertebral compressive fracture (VCF) role in increasing the patients’ death rate and reducing their quality of life, many studies have been conducted for a noninvasive prediction of vertebral compressive strength based on bone mineral density (BMD) determination and recently finite element analysis. In this study, QCT-voxel based nonlinear finite eleme...
متن کاملVARIATIONAL DISCRETIZATION AND MIXED METHODS FOR SEMILINEAR PARABOLIC OPTIMAL CONTROL PROBLEMS WITH INTEGRAL CONSTRAINT
The aim of this work is to investigate the variational discretization and mixed finite element methods for optimal control problem governed by semi linear parabolic equations with integral constraint. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is not discreted. Optimal error estimates in L2 are established for the state...
متن کامل