On the Multi-grid Iteration for the Eigenvalue Problem and the Degree of Interpolation Which It Requires (i)
نویسنده
چکیده
In [8], [10] we presented an approach method to realise a third and fourth order interpolation in two dimensions. In [8] we showed that interpolations of these type can be used as prolongation operator in the multi-grid method and we proved that the accuracy of the multi-grid method can be increased in this way. In this paper we study the optimal degree of the prolongation operator which the second order elliptic eigenvalue problem requires in the point of view of the accuracy. We realise the implementation in Matlab of the multi-grid method with finite difference discretization. Numerical results are also given.
منابع مشابه
Eigenvalue Assignment Of Discrete-Time Linear Systems With State And Input Time-Delays
Time-delays are important components of many dynamical systems that describe coupling or interconnection between dynamics, propagation or transport phenomena, and heredity and competition in population dynamics. The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stabi...
متن کاملA New Inexact Inverse Subspace Iteration for Generalized Eigenvalue Problems
In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax = Bx [Q. Ye and P. Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011) 1697-1715 ]. In particular, the linear convergence property of the inverse subspace iteration is preserved.
متن کاملA Rational Krylov Method Based on Hermite Interpolation for Nonlinear Eigenvalue Problems
This paper proposes a new rational Krylov method for solving the nonlinear eigenvalue problem (NLEP): A(λ)x = 0. The method approximates A(λ) by Hermite interpolation where the degree of the interpolating polynomial and the interpolation points are not fixed in advance. It uses a companion-type reformulation to obtain a linear generalized eigenvalue problem (GEP). To this GEP we apply a rationa...
متن کاملA fuzzy multi-objective model for a project management problem
In this research, the multi-objective project management decision problem with fuzzy goals and fuzzy constraints are considered. We constitute α-cut approach and two various fuzzy goal programming solution methods for solving the Multi-Objective Project Management (MOPM) decision problem under fuzzy environments. The Interactive fuzzy multi-objective linear programming (i-FMOLP) and Weighted Ad...
متن کاملSome results on the symmetric doubly stochastic inverse eigenvalue problem
The symmetric doubly stochastic inverse eigenvalue problem (hereafter SDIEP) is to determine the necessary and sufficient conditions for an $n$-tuple $sigma=(1,lambda_{2},lambda_{3},ldots,lambda_{n})in mathbb{R}^{n}$ with $|lambda_{i}|leq 1,~i=1,2,ldots,n$, to be the spectrum of an $ntimes n$ symmetric doubly stochastic matrix $A$. If there exists an $ntimes n$ symmetric doubly stochastic ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005