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 particul...
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| Language: | en |
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Hindawi Publishing Corporation
2012
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| Online Access: | http://eprints.usm.my/38357/1/Approximation_of_the_pth_Roots_of_a_Matrix_by_Using_Trapezoid_Rule.pdf http://eprints.usm.my/38357/ http://dx.doi.org/10.1155/2012/634698 |
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| author | Sadeghi, Amir Md. Ismail, Ahmad Izani |
| author_facet | Sadeghi, Amir Md. Ismail, Ahmad Izani |
| author_sort | Sadeghi, Amir |
| building | Hamzah Sendut Library |
| collection | Institutional Repository |
| content_provider | Universiti Sains Malaysia |
| content_source | USM Institutional Repository |
| continent | Asia |
| country | Malaysia |
| 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 | my.usm.eprints.38357 |
| institution | Universiti Sains Malaysia |
| language | en |
| publishDate | 2012 |
| publisher | Hindawi Publishing Corporation |
| record_format | eprints |
| spelling | my.usm.eprints.38357 http://eprints.usm.my/38357/ Approximation of the pth Roots of a Matrix by Using Trapezoid Rule Sadeghi, Amir Md. Ismail, Ahmad Izani QA1-939 Mathematics 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. Hindawi Publishing Corporation 2012 Article PeerReviewed application/pdf en http://eprints.usm.my/38357/1/Approximation_of_the_pth_Roots_of_a_Matrix_by_Using_Trapezoid_Rule.pdf Sadeghi, Amir and Md. Ismail, Ahmad Izani (2012) Approximation of the pth Roots of a Matrix by Using Trapezoid Rule. International Journal of Mathematics and Mathematical Sciences, 2012 (634698). pp. 1-13. ISSN 0161-1712 http://dx.doi.org/10.1155/2012/634698 |
| spellingShingle | QA1-939 Mathematics Sadeghi, Amir Md. Ismail, Ahmad Izani Approximation of the pth Roots of a Matrix by Using Trapezoid Rule |
| 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 |
| topic | QA1-939 Mathematics |
| url | http://eprints.usm.my/38357/1/Approximation_of_the_pth_Roots_of_a_Matrix_by_Using_Trapezoid_Rule.pdf http://eprints.usm.my/38357/ http://dx.doi.org/10.1155/2012/634698 |
| url_provider | http://eprints.usm.my/ |