شماره ركورد كنفرانس :
3751
عنوان مقاله :
Valid implementation of the Romberg integration rule to evaluate a definite integral by applying the CADNA library
پديدآورندگان :
Fariborzi Araghi Mohammad Ali fariborzi.araghi@gmail.com Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran. , Noeiaghdam Samad samadnoeiaghdam@gmail.com Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.
كليدواژه :
Stochastic arithmetic , CESTAC method , CADNA library , Romberg integration rule
عنوان كنفرانس :
دومين كنفرانس ملي رياضي: مهندسي پيشرفته با تكنيك هاي رياضي
چكيده فارسي :
Abstract: One of the most important problems in numerical integration is to find the optimal number of iteration in quadrature rules. In this paper, the Romberg integration rule is used to implement in the stochastic arithmetic. To this end, the CESTAC method and the CADNA library are applied. Also, a theorem is proved which can be guaranteed the numerical results. In this theorem, we show the number of common significant digits between the exact and the approximate values is almost equal to the number of common significant digits between two successive approximations. The examples shows the importance of using the stochastic arithmetic in place of the common floating-point arithmetic.
