Convergence Properties of Some Nonlinear Sequence Transformations

نویسندگان

  • Avram Sidi
  • AVRAM SIDI
چکیده

The nonlinear transformations t o accelerate the convergence o f sequences due t o Levin are considered and bounds o n the errors are derived. Convergence theorems for oscillatory and some monotone sequences are proved.

برای دانلود رایگان 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

Nonlinear Sequence Transformations for the Acceleration of Convergence and the Summation of Divergent Series

Slowly convergent series and sequences as well as divergent series occur quite frequently in the mathematical treatment of scientific problems. In this report, a large number of mainly nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series are discussed. Some of the sequence transformations of this report as for instance Wynn’s ǫ algorithm o...

متن کامل

Nonlinear Sequence Transformations: Computational Tools for the Acceleration of Convergence and the Summation of Divergent Series

Convergence problems occur abundantly in all branches of mathematics or in the mathematical treatment of the sciences. Sequence transformations are principal tools to overcome convergence problems of the kind. They accomplish this by converting a slowly converging or diverging input sequence {sn} ∞ n=0 into another sequence {s ′ n }∞ n=0 with hopefully better numerical properties. Padé approxim...

متن کامل

On the approximation by Chlodowsky type generalization of (p,q)-Bernstein operators

In the present article, we introduce Chlodowsky variant of $(p,q)$-Bernstein operators and compute the moments for these operators which are used in proving our main results. Further, we study some approximation properties of these new operators, which include the rate of convergence using usual modulus of continuity and also the rate of convergence when the function $f$ belongs to the class Li...

متن کامل

Nonlinear Hybrid Procedures and Xed Point Iterations

Let (x n) and (^ x n) be two vector sequences converging to a common limit. First, we shall deene nonlinear hybrid procedures which consist of constructing a new vector sequence (y n) with better convergence properties than (x n) and (^ x n). Then, this procedure is used for accelerating the convergence of a given sequence and applied to the construction of xed point methods. New methods are de...

متن کامل

Scalar Levin-type Sequence Transformations

Sequence transformations are important tools for the convergence acceleration of slowly convergent scalar sequences or series and for the summation of divergent series. The basic idea is to construct from a given sequence { sn} a new sequence { s ′ n} = T ({ sn} ) where each s ′ n depends on a finite number of elements sn1 , . . . , snm . Often, the sn are the partial sums of an infinite series...

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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007