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Paper Information

Journal:   IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A- SCIENCE   2014 , Volume 38 , Number A2; Page(s) 123 To 132.
 
Paper: 

CHAIN LEAST SQUARES METHOD AND ILL-POSED PROBLEMS

 
 
Author(s):  BABOLIAN E., ABDOLLAHI A.*, SHAHMORAD S.
 
* DEPARTMENT OF MATHEMATICS, SCIENCE AND RESEARCH BRANCH, ISLAMIC AZAD UNIVERSITY, TEHRAN, IRAN
 
Abstract: 

The main purpose of this article is to increase the efficiency of the least squares method in numerical solution of ill-posed functional and physical equations. Determining the least squares of a given function in an arbitrary set is often an ill-posed problem. In this article, by defining artificial constraint and using Lagrange multipliers method, the attempt is to turn n-dimensional least squares problems into (n-1) ones, in a way that the condition number of the corresponding system with(n-1) -dimensional problem will be low. At first, the new method is introduced for2 and 3-term basis, then the presented method is generalized for n-term basis. Finally, the numerical solution of some ill-posed problems like Fredholm integral equations of the first kind and singularly perturbed linear Fredholm integral equations of the second kind are approximated by chain least squares method. Numerical comparisons indicate that the chain least squares method yields accurate and stable approximations in many cases.

 
Keyword(s): LAGRANGE MULTIPLIERS METHOD, CHAIN LEAST SQUARES, ILL-POSED PROBLEM, INTEGRAL EQUATIONS
 
 
References: 
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Click to Cite.
APA: Copy

BABOLIAN, E., & ABDOLLAHI, A., & SHAHMORAD, S. (2014). CHAIN LEAST SQUARES METHOD AND ILL-POSED PROBLEMS. IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A- SCIENCE, 38(A2), 123-132. https://www.sid.ir/en/journal/ViewPaper.aspx?id=402579



Vancouver: Copy

BABOLIAN E., ABDOLLAHI A., SHAHMORAD S.. CHAIN LEAST SQUARES METHOD AND ILL-POSED PROBLEMS. IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A- SCIENCE. 2014 [cited 2021May12];38(A2):123-132. Available from: https://www.sid.ir/en/journal/ViewPaper.aspx?id=402579



IEEE: Copy

BABOLIAN, E., ABDOLLAHI, A., SHAHMORAD, S., 2014. CHAIN LEAST SQUARES METHOD AND ILL-POSED PROBLEMS. IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A- SCIENCE, [online] 38(A2), pp.123-132. Available: https://www.sid.ir/en/journal/ViewPaper.aspx?id=402579.



 
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