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:: Volume 7, Issue 2 (Vol.7, No. 2, Summer 2021) ::
mr 2021, 7(2): 389-396 Back to browse issues page
Numerical Stability in Complex Summation
Hassan Majidian 1, Medina Firouzi2, Amjad Alipanah2
1- Department of Encyclopedia Researches, Institute for Humanities and Cultural Studies , h.majidian@ihcs.ac.ir
2- Department of Mathematics, University of Kurdistan
Abstract:   (207 Views)
The natural and practical condition numbers for summation of complex numbers are introduced. These numbers measure the effect of loss of significant digits on the round-off error when computing a sum in floating point arithmetic. The relationship between the natural and practical condition numbers and their size are studied. It is shown that the practical condition number is equal to one when all the summands lie in one of the quadrants of the complex plane. Also, an upper bound for the natural condition number is obtained when the summands lie in a sector with an angle less than or equal to pi/2../files/site1/files/72/16Abstract.pdf
Keywords: complex summation, condition number, numerical stability, cancellation.
Full-Text [PDF 424 kb]   (44 Downloads)    
Type of Study: S | Subject: alg
Received: 2018/10/17 | Accepted: 2019/11/19 | Published: 2021/09/1 | ePublished: 2021/09/1
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Majidian H, Firouzi M, Alipanah A. Numerical Stability in Complex Summation. mr. 2021; 7 (2) :389-396
URL: http://mmr.khu.ac.ir/article-1-2859-en.html


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Volume 7, Issue 2 (Vol.7, No. 2, Summer 2021) Back to browse issues page
پژوهش‌های ریاضی Mathematical Researches
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