scholarly journals Explicit forms of weighted quadrature rules with geometric nodes

2011 ◽  
Vol 53 (5-6) ◽  
pp. 1133-1139 ◽  
Author(s):  
Mohammad Masjed-Jamei ◽  
Gradimir V. Milovanović ◽  
M.A. Jafari
Keyword(s):  
Quadrature Rules ◽  
Weighted Quadrature

A unified representation for some interpolation formulas

Analysis ◽  
2020 ◽  
Vol 40 (3) ◽  
pp. 113-125
Author(s):  
Mohammad Masjed-Jamei ◽  
Zahra Moalemi ◽  
Wolfram Koepf
Keyword(s):  
Existence And Uniqueness ◽  
Lagrange Interpolation ◽  
Quadrature Rules ◽  
Numerical Examples ◽  
Weighted Quadrature

AbstractAs an extension of Lagrange interpolation, we introduce a class of interpolation formulas and study their existence and uniqueness. In the sequel, we consider some particular cases and construct the corresponding weighted quadrature rules. Numerical examples are finally given and compared.

scholarly journals A Note on Finite Quadrature Rules with a Kind of Freud Weight Function

2009 ◽  
Vol 2009 ◽  
pp. 1-8
Author(s):  
Kamal Aghigh ◽  
M. Masjed-Jamei
Keyword(s):  
Weight Function ◽  
Quadrature Rule ◽  
Quadrature Rules ◽  
Zeros Of Polynomials ◽  
Freud Weight ◽  
Weighted Quadrature

We introduce a finite class of weighted quadrature rules with the weight function on as , where are the zeros of polynomials orthogonal with respect to the introduced weight function, are the corresponding coefficients, and is the error value. We show that the above formula is valid only for the finite values of . In other words, the condition must always be satisfied in order that one can apply the above quadrature rule. In this sense, some numerical and analytic examples are also given and compared.

scholarly journals Weighted quadrature rules for finite element methods

2009 ◽  
Vol 227 (1) ◽  
pp. 93-101 ◽  
Author(s):  
Saulo P. Oliveira ◽  
Alexandre L. Madureira ◽  
Frederic Valentin
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Quadrature Rules ◽  
Weighted Quadrature

Weighted quadrature rules via Grüss type inequalities for weighted Lp spaces

2015 ◽  
Vol 264 ◽  
pp. 1-12
Author(s):  
A. Aglić Aljinović ◽  
J. Pečarić ◽  
S. Tipurić-Spužević
Keyword(s):  
Quadrature Rules ◽  
Lp Spaces ◽  
Grüss Type Inequalities ◽  
Weighted Quadrature

Weighted quadrature rules with weight function on [0,∞)

2006 ◽  
Vol 180 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Mehdi Dehghan ◽  
M. Masjed-Jamei ◽  
M.R. Eslahchi
Keyword(s):  
Weight Function ◽  
Quadrature Rules ◽  
Weighted Quadrature

A note on weighted quadrature rules

2015 ◽  
Vol 40 (17) ◽  
pp. 6103-6113 ◽  
Author(s):  
Mohammad Masjed-Jamei ◽  
Iván Area
Keyword(s):  
Quadrature Rules ◽  
Weighted Quadrature

scholarly journals On Appel-Type Quadrature Rules

2002 ◽  
Vol 9 (3) ◽  
pp. 405-412
Author(s):  
C. Belingeri ◽  
B. Germano
Keyword(s):  
Remainder Term ◽  
Quadrature Rule ◽  
Bernoulli Numbers ◽  
Quadrature Rules ◽  
Rule Based ◽  
Numerical Example ◽  
The Given ◽  
Derivatives Of

Abstract The Radon technique is applied in order to recover a quadrature rule based on Appel polynomials and the so called Appel numbers. The relevant formula generalizes both the Euler-MacLaurin quadrature rule and a similar rule using Euler (instead of Bernoulli) numbers and even (instead of odd) derivatives of the given function at the endpoints of the considered interval. In the general case, the remainder term is expressed in terms of Appel numbers, and all derivatives appear. A numerical example is also included.

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