Complexity of Path-Following Methods for the Eigenvalue Problem
A unitarily invariant projective framework is introduced to analyze the complexity of path-following methods for the eigenvalue problem. A condition number, and its relation to the distance to ill-posedness, is given. A Newton map appropriate for this context is defined, and a version of Smale’s γ -...
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| Veröffentlicht in: | Foundations of computational mathematics 2014-04, Vol.14 (2), p.185-236 |
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| container_title | Foundations of computational mathematics |
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| creator | Armentano, Diego |
| description | A unitarily invariant projective framework is introduced to analyze the complexity of path-following methods for the eigenvalue problem. A condition number, and its relation to the distance to ill-posedness, is given. A Newton map appropriate for this context is defined, and a version of Smale’s
γ
-theorem is proven. The main result of this paper bounds the complexity of path-following methods in terms of the length of the path in the condition metric. |
| doi_str_mv | 10.1007/s10208-013-9185-5 |
| format | Article |
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γ
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γ
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Applications of Mathematics Complexity Computation Computer Science Economics Eigenvalues Foundations Functions, Inverse Homotopy theory Invariants Linear and Multilinear Algebras Math Applications in Computer Science Mathematical analysis Mathematical models Mathematical research Mathematics Mathematics and Statistics Matrix Theory Numerical Analysis Polynomials Texts Topological manifolds |
| title | Complexity of Path-Following Methods for the Eigenvalue Problem |
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