Approximation of the pth Roots of a Matrix by Using Trapezoid Rule
The computation of the roots of positive definite matrices arises in nuclear magnetic resonance, control theory, lattice quantum chromo-dynamics (QCD), and several other areas of applications. The Cauchy integral theorem which arises in complex analysis can be used for computing f(A), in particular...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/634698 |
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| _version_ | 1849435100138176512 |
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| author | Amir Sadeghi Ahmad Izani Md. Ismail |
| author_facet | Amir Sadeghi Ahmad Izani Md. Ismail |
| author_sort | Amir Sadeghi |
| collection | DOAJ |
| description | The computation of the roots of positive definite matrices arises in nuclear magnetic resonance, control theory, lattice quantum chromo-dynamics (QCD), and several other areas of applications. The Cauchy integral theorem which arises in complex analysis can be used for computing f(A), in particular the roots of A, where A is a square matrix. The Cauchy integral can be approximated by using the trapezoid rule. In this paper, we aim to give a brief overview of the computation of roots of positive definite matrices by employing integral representation. Some numerical experiments are given to illustrate the theoretical results. |
| format | Article |
| id | doaj-art-5be9189ddd754a869a67e8bd86b9a2dd |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-5be9189ddd754a869a67e8bd86b9a2dd2025-08-20T03:26:25ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/634698634698Approximation of the pth Roots of a Matrix by Using Trapezoid RuleAmir Sadeghi0Ahmad Izani Md. Ismail1School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, MalaysiaSchool of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, MalaysiaThe computation of the roots of positive definite matrices arises in nuclear magnetic resonance, control theory, lattice quantum chromo-dynamics (QCD), and several other areas of applications. The Cauchy integral theorem which arises in complex analysis can be used for computing f(A), in particular the roots of A, where A is a square matrix. The Cauchy integral can be approximated by using the trapezoid rule. In this paper, we aim to give a brief overview of the computation of roots of positive definite matrices by employing integral representation. Some numerical experiments are given to illustrate the theoretical results.http://dx.doi.org/10.1155/2012/634698 |
| spellingShingle | Amir Sadeghi Ahmad Izani Md. Ismail Approximation of the pth Roots of a Matrix by Using Trapezoid Rule International Journal of Mathematics and Mathematical Sciences |
| title | Approximation of the pth Roots of a Matrix by Using Trapezoid Rule |
| title_full | Approximation of the pth Roots of a Matrix by Using Trapezoid Rule |
| title_fullStr | Approximation of the pth Roots of a Matrix by Using Trapezoid Rule |
| title_full_unstemmed | Approximation of the pth Roots of a Matrix by Using Trapezoid Rule |
| title_short | Approximation of the pth Roots of a Matrix by Using Trapezoid Rule |
| title_sort | approximation of the pth roots of a matrix by using trapezoid rule |
| url | http://dx.doi.org/10.1155/2012/634698 |
| work_keys_str_mv | AT amirsadeghi approximationofthepthrootsofamatrixbyusingtrapezoidrule AT ahmadizanimdismail approximationofthepthrootsofamatrixbyusingtrapezoidrule |