On the Divergent Properties of Two–sided Sor Weierstrass Method
نویسندگان
چکیده
In this paper the convergence properties of the two-side successive over-relaxation (TSSOR) method of Weierstrass’ type is discussed. Initial conditions under which this method is divergent are stated. The main theorem generalizes some recent results concerning divergent properties of simultaneous methods for finding polynomial zeros. Let f(x) = x + an−1xn−1 + · · ·+ a1x+ a0 be a monic polynomial with simple real roots ξ1 < ξ2 < . . . < ξn. We assume that the roots are located in n nonintersecting real intervals X i = [xi , x 0 i ], i = 1, 2, . . . , n, that is, X 0 i ∩ X j = ∅ for i = j and ξi ∈ X i for i = 1, 2, . . . , n. In this paper we are concerned with the two-sided method (1) x i = x k i − hk f(xi ) i−1 ∏
منابع مشابه
ON THE POWER FUNCTION OF THE LRT AGAINST ONE-SIDED AND TWO-SIDED ALTERNATIVES IN BIVARIATE NORMAL DISTRIBUTION
This paper addresses the problem of testing simple hypotheses about the mean of a bivariate normal distribution with identity covariance matrix against restricted alternatives. The LRTs and their power functions for such types of hypotheses are derived. Furthermore, through some elementary calculus, it is shown that the power function of the LRT satisfies certain monotonicity and symmetry p...
متن کاملCHEBYSHEV ACCELERATION TECHNIQUE FOR SOLVING FUZZY LINEAR SYSTEM
In this paper, Chebyshev acceleration technique is used to solve the fuzzy linear system (FLS). This method is discussed in details and followed by summary of some other acceleration techniques. Moreover, we show that in some situations that the methods such as Jacobi, Gauss-Sidel, SOR and conjugate gradient is divergent, our proposed method is applicable and the acquired results are illustrate...
متن کاملDetermining the order of minimal realization of descriptor systems without use of the Weierstrass canonical form
A common method to determine the order of minimal realization of a continuous linear time invariant descriptor system is to decompose it into slow and fast subsystems using the Weierstrass canonical form. The Weierstrass decomposition should be avoided because it is generally an ill-conditioned problem that requires many complex calculations especially for high-dimensional systems. The present ...
متن کاملThe new implicit finite difference scheme for two-sided space-time fractional partial differential equation
Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. S...
متن کاملSimultaneous Multi-Skilled Worker Assignment and Mixed-Model Two-Sided Assembly Line Balancing
This paper addresses a multi-objective mathematical model for the mixed-model two-sided assembly line balancing and worker assignment with different skills. In this problem, the operation time of each task is dependent on the skill of the worker. The following objective functions are considered in the mathematical model: (1) minimizing the number of mated-stations (2), minimizing the number of ...
متن کامل