scholarly journals Gaussian quadrature rules and numerical examples for strong extensions of mass distribution functions

1999 ◽  
Vol 105 (1-2) ◽  
pp. 317-326 ◽  
Author(s):  
Philip E. Gustafson ◽  
Brian A. Hagler
Keyword(s):  
Mass Distribution ◽  
Gaussian Quadrature ◽  
Distribution Functions ◽  
Quadrature Rules ◽  
Numerical Examples

scholarly journals Generalized Gaussian quadratures for integrals with logarithmic singularity

Filomat ◽  
2016 ◽  
Vol 30 (4) ◽  
pp. 1111-1126 ◽  
Author(s):  
Gradimir Milovanovic
Keyword(s):  
Logarithmic Singularity ◽  
Gaussian Quadrature ◽  
Quadrature Rules ◽  
Quadrature Formulas ◽  
Short Account ◽  
Numerical Examples ◽  
Gaussian Quadrature Formulas ◽  
Gaussian Quadratures ◽  
Logarithmic Singularities

A short account on Gaussian quadrature rules for integrals with logarithmic singularity, as well as some new results for weighted Gaussian quadrature formulas with respect to generalized Gegenbauer weight x |? |x|(1-x2)?, ? > -1, on (-1,1), which are appropriated for functions with and without logarithmic singularities, are considered. Methods for constructing such kind of quadrature formulas and some numerical examples are included.

scholarly journals An Algorithm for the Numerical Evaluation of Certain Finite Part Integrals

2011 ◽  
Vol 2011 ◽  
pp. 1-21
Author(s):  
Samir A. Ashour ◽  
Hany M. Ahmed
Keyword(s):  
Numerical Evaluation ◽  
Gaussian Quadrature ◽  
Quadrature Rules ◽  
Finite Part ◽  
Cauchy Principal ◽  
Cauchy Principal Value ◽  
Cauchy Principal Value Integrals ◽  
Principal Value

Many algorithms that have been proposed for the numerical evaluation of Cauchy principal value integrals are numerically unstable. In this work we present some formulae to evaluate the known Gaussian quadrature rules for finite part integrals , and extend Clenshow's algorithm to evaluate these integrals in a stable way.

scholarly journals Application of MATLAB Symbolic Maths with Variable Precision Arithmetic (VPA) to Compute Some High Order Gauss Legendre Quadrature Rules

1970 ◽  
Vol 29 ◽  
pp. 117-125
Author(s):  
HT Rathod ◽  
RD Sathish ◽  
Md Shafiqul Islam ◽  
Arun Kumar Gali
Keyword(s):  
Gaussian Quadrature ◽  
High Order ◽  
Quadrature Rules ◽  
Zeros Of Polynomials ◽  
Matlab Program ◽  
Present Context ◽  
First Time ◽  
Legendre Quadrature ◽  
Weight Coefficients ◽  
Integration Rules

Gauss Legendre Quadrature rules are extremely accurate and they should be considered seriously when many integrals of similar nature are to be evaluated. This paper is concerned with the derivation and computation of numerical integration rules for the three integrals: (See text for formulae) which are dependent on the zeros and the squares of the zeros of Legendre Polynomial and is quite well known in the Gaussian Quadrature theory. We have developed the necessary MATLAB programs based on symbolic maths which can compute the sampling points and the weight coefficients and are reported here upto 32 – digits accuracy and we believe that they are reported to this accuracy for the first time. The MATLAB programs appended here are based on symbolic maths. They are very sophisticated and they can compute Quadrature rules of high order, whereas one of the recent MATLAB program appearing in reference [21] can compute Gauss Legendre Quadrature rules upto order twenty, because the zeros of Legendre polynomials cannot be computed to desired accuracy by MATLAB routine roots (……..). Whereas we have used the MATLAB routine solve (……..) to find zeros of polynomials which is very efficient. This is worth noting in the present context. GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 29 (2009) 117-125  DOI: http://dx.doi.org/10.3329/ganit.v29i0.8521 

SOME EXTENSIONS OF THE RESIDUAL LIFETIME AND ITS CONNECTION TO THE CUMULATIVE RESIDUAL ENTROPY

2011 ◽  
Vol 26 (1) ◽  
pp. 129-146 ◽  
Author(s):  
Stella Kapodistria ◽  
Georgios Psarrakos
Keyword(s):  
Random Variables ◽  
Distribution Functions ◽  
Residual Entropy ◽  
Residual Lifetime ◽  
Numerical Examples ◽  
Tail Distribution ◽  
Cumulative Residual Entropy ◽  
Recursive Formulas ◽  
Cumulative Residual

In this article we present a sequence of random variables with weighted tail distribution functions, constructed based on the relevation transform. For this sequence, we prove several recursive formulas and connections to the residual entropy through the unifying framework of the Dickson–Hipp operator. We also give some numerical examples to evaluate our results.

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