Numerical Stability in Complex Summation
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 a...
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| Format: | Article |
| Language: | fas |
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Kharazmi University
2021-09-01
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| Series: | پژوهشهای ریاضی |
| Subjects: | |
| Online Access: | http://mmr.khu.ac.ir/article-1-2859-en.html |
| _version_ | 1797871653001101312 |
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| author | Hassan Majidian Medina Firouzi Amjad Alipanah |
| author_facet | Hassan Majidian Medina Firouzi Amjad Alipanah |
| author_sort | Hassan Majidian |
| collection | DOAJ |
| description | 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 |
| first_indexed | 2024-04-10T00:47:15Z |
| format | Article |
| id | doaj.art-71213d38dd5d4936abce0206465bee45 |
| institution | Directory Open Access Journal |
| issn | 2588-2546 2588-2554 |
| language | fas |
| last_indexed | 2024-04-10T00:47:15Z |
| publishDate | 2021-09-01 |
| publisher | Kharazmi University |
| record_format | Article |
| series | پژوهشهای ریاضی |
| spelling | doaj.art-71213d38dd5d4936abce0206465bee452023-03-13T19:22:49ZfasKharazmi Universityپژوهشهای ریاضی2588-25462588-25542021-09-0172389396Numerical Stability in Complex SummationHassan Majidian0Medina Firouzi1Amjad Alipanah2 Department of Encyclopedia Researches, Institute for Humanities and Cultural Studies Department of Mathematics, University of Kurdistan Department of Mathematics, University of Kurdistan 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.pdfhttp://mmr.khu.ac.ir/article-1-2859-en.htmlcomplex summationcondition numbernumerical stabilitycancellation. |
| spellingShingle | Hassan Majidian Medina Firouzi Amjad Alipanah Numerical Stability in Complex Summation پژوهشهای ریاضی complex summation condition number numerical stability cancellation. |
| title | Numerical Stability in Complex Summation |
| title_full | Numerical Stability in Complex Summation |
| title_fullStr | Numerical Stability in Complex Summation |
| title_full_unstemmed | Numerical Stability in Complex Summation |
| title_short | Numerical Stability in Complex Summation |
| title_sort | numerical stability in complex summation |
| topic | complex summation condition number numerical stability cancellation. |
| url | http://mmr.khu.ac.ir/article-1-2859-en.html |
| work_keys_str_mv | AT hassanmajidian numericalstabilityincomplexsummation AT medinafirouzi numericalstabilityincomplexsummation AT amjadalipanah numericalstabilityincomplexsummation |