The Arnoldi method in the light of Homotopic Deviation theory
نویسنده
چکیده
This paper aims at providing an algorithmic understanding of the “convergence” of Krylov-type methods which relies on asymptotic properties at 0 and ∞. The classical normwise (or analytic) perturbation approach correponds to the limit towards 0. We complement this analysis by the structural perturbation approach provided by the limit to ∞ in the Homotopic Deviation theory. We easily get back the classical results when the homotopy parameter h tends to 0. But we get new results by letting |h| → ∞, leading to new insights on long standing algorithmic issues.
منابع مشابه
Some new restart vectors for explicitly restarted Arnoldi method
The explicitly restarted Arnoldi method (ERAM) can be used to find some eigenvalues of large and sparse matrices. However, it has been shown that even this method may fail to converge. In this paper, we present two new methods to accelerate the convergence of ERAM algorithm. In these methods, we apply two strategies for the updated initial vector in each restart cycles. The implementation of th...
متن کاملResidual Arnoldi Methods : Theory ,
Title of dissertation: Residual Arnoldi Methods : Theory, Package, and Experiments Che-Rung Lee, Doctor of Philosophy, 2007 Dissertation directed by: Professor G.W. Stewart Department of Computer Science This thesis is concerned with the solution of large-scale eigenvalue problems. Although there are good algorithms for solving small dense eigenvalue problems, the large-scale eigenproblem has m...
متن کاملThe Interpretive Analysis of the Verse "کُلٌّ فی فَلَکٍ یَسْبَحُون" (All glide along, each in its own orbit) in Light of the Theory of Volume of Space
In several verses, the Holy Qur'an refers to astronomy and the heavenly bodies, and raises some issues such as the relations and interactions of the heavenly bodies and their surrounding environment. Among these verses are verse 40 of Surah al-Yasin and verse 33 of Surah al-Anbiyah which express the positional and motional characteristics of the Sun and the Moon by choosing specific and purpose...
متن کاملINVESTIGATING THE VALIDITY OF PHD ENTRANCE EXAM OF ELT IN IRAN IN LIGHT OF ARGUMENT-BASED VALIDITY AND THEORY OF ACTION
Although some piecemeal efforts have been made to investigate the validity and use of the Iranian PhD exam, no systematic project has been specifically carried out in this regard. The current study, hence, tried to attend to this void. As such, to ensure a balanced focus on test interpretation and test consequence, and to track evidence derived from a mixed–method study on the validity of Irani...
متن کاملMultigrid Arnoldi for Eigenvalues
A new approach is given for computing eigenvalues and eigenvectors of large matrices. Multigrid is combined with the Arnoldi method in order to solve difficult problems. First, a two-grid method computes eigenvalues on a coarse grid and improves them on the fine grid. On the fine grid, an Arnoldi-type method is used that, unlike standard Arnoldi methods, can accept initial approximate eigenvect...
متن کامل