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CONVERGENCE ACCELERATION OF HERMITE-FEJ RPOLYNOMIALS BASED ON LEGENDRE NODES INTHE INTERVAL [-1,1]

Author: Hussain Ali Al-Juboury
Journal: Al-Nahrain Journal of Science مجلة النهرين للعلوم ISSN: (print)26635453,(online)26635461 Year: 2010 Volume: 13 Issue: 1 Pages: 150-156
Publisher: Al-Nahrain University جامعة النهرين

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Abstract

The rate of uniform convergence for Hermite-Fejer polynomials to any continuous function f(x) in each closed sub-interval of (-1,1) has been given by Schonhage in 1971 by means of estimating the rate of convergence. The present paper deals with the acceleration of convergence and the rate of convergence by improving the estimate given by Schonhage, throughout two parallel ways, firstly, by use of the averaged moduli of smoothness or -moduli that gives much better estimation than that of the moduli of continuity or -moduli. Secondly, by make use of the necessary and sufficient conditions that we borrow from Szego in 1959 together with the well-known Fejer's identity (3.8) and the properties of -moduli in addition to some known results that have been given by Murray Spiegel in 1981 pp299-345.


Article
The Collocation Method for Solving the Linear Fredholm Integral Equation of the Second Kind Using Bernstein Polynomials
استخدام متعددات الحدود برتشتاين كل المعادلات فردهولم التكاملية من النوع الثاني

Authors: Hussain Ali Al -Juboury --- Shymaa Hussain Salih
Journal: Engineering and Technology Journal مجلة الهندسة والتكنولوجيا ISSN: 16816900 24120758 Year: 2010 Volume: 28 Issue: 3 Pages: 621-625
Publisher: University of Technology الجامعة التكنولوجية

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Abstract

Integral equation of the second kind which has, extensively, been solved bydifferent ways, but not this one that deals with the collocation method using Bernsteinpolynomials together with some useful examples to declare the method.

وباستخدام متعددات الحدود برنشتاين (collocation method) بدلالة طريقة التوضعوجدنا حلاً لمعادلة فردهوم التكاملية من النوع الثاني واعطيت بعض الامثلة المفيدة في توضيحالطريقة المذكورة.

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