On the Application of Iterative Methods of Nondifferentiable Optimization to Some Problems of Approximation Theory
المؤلف
المصدر
Mathematical Problems in Engineering
العدد
المجلد 2014، العدد 2014 (31 ديسمبر/كانون الأول 2014)، ص ص. 1-10، 10ص.
الناشر
Hindawi Publishing Corporation
تاريخ النشر
2014-11-27
دولة النشر
مصر
عدد الصفحات
10
التخصصات الرئيسية
الملخص EN
We consider the data fitting problem, that is, the problem of approximating a function of several variables, given by tabulated data, and the corresponding problem for inconsistent (overdetermined) systems of linear algebraic equations.
Such problems, connected with measurement of physical quantities, arise, for example, in physics, engineering, and so forth.
A traditional approach for solving these two problems is the discrete least squares data fitting method, which is based on discrete l 2 -norm.
In this paper, an alternative approach is proposed: with each of these problems, we associate a nondifferentiable (nonsmooth) unconstrained minimization problem with an objective function, based on discrete l 1 - and/or l ∞ -norm, respectively; that is, these two norms are used as proximity criteria.
In other words, the problems under consideration are solved by minimizing the residual using these two norms.
Respective subgradients are calculated, and a subgradient method is used for solving these two problems.
The emphasis is on implementation of the proposed approach.
Some computational results, obtained by an appropriate iterative method, are given at the end of the paper.
These results are compared with the results, obtained by the iterative gradient method for the corresponding “differentiable” discrete least squares problems, that is, approximation problems based on discrete l 2 -norm.
نمط استشهاد جمعية علماء النفس الأمريكية (APA)
Stefanov, Stefan M.. 2014. On the Application of Iterative Methods of Nondifferentiable Optimization to Some Problems of Approximation Theory. Mathematical Problems in Engineering،Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-1044036
نمط استشهاد الجمعية الأمريكية للغات الحديثة (MLA)
Stefanov, Stefan M.. On the Application of Iterative Methods of Nondifferentiable Optimization to Some Problems of Approximation Theory. Mathematical Problems in Engineering No. 2014 (2014), pp.1-10.
https://search.emarefa.net/detail/BIM-1044036
نمط استشهاد الجمعية الطبية الأمريكية (AMA)
Stefanov, Stefan M.. On the Application of Iterative Methods of Nondifferentiable Optimization to Some Problems of Approximation Theory. Mathematical Problems in Engineering. 2014. Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-1044036
نوع البيانات
مقالات
لغة النص
الإنجليزية
الملاحظات
Includes bibliographical references
رقم السجل
BIM-1044036
قاعدة معامل التأثير والاستشهادات المرجعية العربي "ارسيف Arcif"
أضخم قاعدة بيانات عربية للاستشهادات المرجعية للمجلات العلمية المحكمة الصادرة في العالم العربي
تقوم هذه الخدمة بالتحقق من التشابه أو الانتحال في الأبحاث والمقالات العلمية والأطروحات الجامعية والكتب والأبحاث باللغة العربية، وتحديد درجة التشابه أو أصالة الأعمال البحثية وحماية ملكيتها الفكرية. تعرف اكثر