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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Publishing Corporation
2012
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| Subjects: | |
| Online Access: | http://eprints.usm.my/38357/ http://eprints.usm.my/38357/1/Approximation_of_the_pth_Roots_of_a_Matrix_by_Using_Trapezoid_Rule.pdf |
| Summary: | 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. |
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