Componentwise Error Estimates for Solutions Obtained by Stationary Iterative Methods

نویسنده

  • Shinya Miyajima
چکیده

In stationary iterative methods for solving linear systems Ax = b, the iteration x = Hx + c, where H and c are the iteration matrix derived from A and the vector derived from A and b, respectively, is executed for an initial vector x. We present a theorem which yields componentwise error estimates for x, and clarify the relation between our result and a previous result.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Componentwise Error Analysis for Stationary Iterative Methods∗

How small can a stationary iterative method for solving a linear system Ax = b make the error and the residual in the presence of rounding errors? We give a componentwise error analysis that provides an answer to this question and we examine the implications for numerical stability. The Jacobi, Gauss-Seidel and successive overrelaxation methods are all found to be forward stable in a componentw...

متن کامل

On Optimal Solution of Interval Linear Equations

For interval linear algebraic systems Ax = b, the problem is considered of componentwise evaluation of the set Σ∃∃(A,b) = {Ab | A∈A, b∈b } formed by all solutions of Ax = b when A and b vary independently in A and b, respectively. An iterative PSS algorithm is introduced that computes optimal (exact) componentwise estimates of Σ∃∃ and its convergence is proved under fairly general conditions on...

متن کامل

Componentwise Perturbation Theory for Linear Systems With Multipte Right-Hand Sides

Existing definitions of componentwise backward error and componentwise condi tion number for linear systems are extended to systems with multiple right-hand sides and to a general class of componentwise measure of perturbations involving Holder p-norms. It is shown that for a system of order n with r right-hand sides, the componentwise backward error can be computed by finding the minimum p-nor...

متن کامل

On Approximate Stationary Radial Solutions for a Class of Boundary Value Problems Arising in Epitaxial Growth Theory

In this paper, we consider a non-self-adjoint, singular, nonlinear fourth order boundary value problem which arises in the theory of epitaxial growth. It is possible to reduce the fourth order equation to a singular boundary value problem of second order given by w''-1/r w'=w^2/(2r^2 )+1/2 λ r^2. The problem depends on the parameter λ and admits multiple solutions. Therefore, it is difficult to...

متن کامل

On the Numerical Behavior of Matrix Splitting Iteration Methods for Solving Linear Systems

We study the numerical behavior of stationary one-step or two-step matrix splitting iteration methods for solving large sparse systems of linear equations. We show that inexact solutions of inner linear systems associated with the matrix splittings may considerably influence the accuracy of the approximate solutions computed in finite precision arithmetic. For a general stationary matrix splitt...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Reliable Computing

دوره 16  شماره 

صفحات  -

تاریخ انتشار 2012