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MQ-Radial Basis Functions Center Nodes Selection with PROMETHEE Technique | ||
Control and Optimization in Applied Mathematics | ||
مقاله 3، دوره 3، شماره 2، فروردین 2018، صفحه 27-47 اصل مقاله (1.12 M) | ||
نوع مقاله: Research Article | ||
شناسه دیجیتال (DOI): 10.30473/coam.2019.46609.1117 | ||
نویسندگان | ||
Farhad Hadinejad* 1؛ Saeed Kazem2 | ||
1Phd of Operation Research Management, Allameh Tabataba'i University and Assistant professor, Imam Ali University, Tehran, Iran | ||
2Department of Applied Mathematics, Amirkabir University of Technology, No. 424, Hafez Ave., 15914, Tehran, Iran | ||
چکیده | ||
In this paper, we decide to select the best center nodes of radial basis functions by applying the Multiple Criteria Decision Making (MCDM) techniques. Two methods based on radial basis functions to approximate the solution of partial differential equation by using collocation method are applied. The first is based on the Kansa's approach, and the second is based on the Hermite interpolation. In addition, by choosing five sets of center nodes: Uniform grid, Cartesian, Chebyshev, Legendre and Legendre-Gauss-Lobato (LGL) as alternatives and achieving the error, the condition number of interpolation matrix and memory time as criteria, rating of cases with the help of PROMETHEE technique is obtained. In the end, the best center nodes and method is selected according to the rankings. This ranking shows that Hermite interpolation by using non-uniform nodes as center nodes is more suitable than Kansa's approach with each center node. | ||
کلیدواژهها | ||
Multiple Criteria Decision Making؛ Radial basis functions؛ PROMETHEE؛ Hermite interpolation؛ Optimal selecting | ||
عنوان مقاله [English] | ||
انتخاب نقاط مرکزی توابع پایه ای شعاعی با کمک تکنیک پرامیتی | ||
نویسندگان [English] | ||
فرهاد هادی نژاد1؛ سعید کاظم2 | ||
1دانش آموخته دکترای مدیریت گرایش OR از دانشگاه علامه طباطبائی و استادیار گروه مدیریت دانشگاه امام علی (ع)، | ||
2دانش آموخته دکتری دانشگاه صنعتی امیرکبیر، گروه ریاضی کاربردی، ایران، تهران، دانشگاه صنعتی امیرکبیر | ||
چکیده [English] | ||
در این مقاله تلاش می شود که بهترین نقاط مرکزی توابع پایه شعاعی را با استفاده از تکنیکهای تصمیمگیری چند معیاره (MCDM) انتخاب کنیم. دو روش مبتنی بر توابع پایهای شعاعی برای حل معادلات دیفرانسیل با مشتقات جزئی مورد استفاده قرار میگیرد. روش اول مبتنی بر روش کانسا و روش دوم مبتنی بر درونیابی هرمیتی میباشند. علاوه بر این، با انتخاب پنج مجموعه از نقاط مرکزی: کارتزین، همفاصله، چبیشف، لژاندر و لژاندر گاوس لوباتو به عنوان گزینههای تحقیق و متغیرهای: خطا، عدد حالت ماتریس درونیاب و زمان اجرا به عنوان معیارهای تاثیرگذار، گزینهها با کمک تکنیک پرامیتی رتبهبندی گردیدند. در نهایت بهترین نقاط مرکزی بر اساس رتبه بدست آمده انتخاب گردید. این رتبهبندی نشان میدهد که روش درونیابی هرمیتی با استفاده از نقاط غیر یکنواخت به عنوان نقاط مرکزی مناسبتر از روش کانسا با هر نقطه مرکزی است. | ||
کلیدواژهها [English] | ||
تصمیم گیری چندمعیاره, توابع مرکزی شعاعی, پرامیتی, درون یابی هرمیت, انتخاب بهینه | ||
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