Complexity of Path-Following Methods for the Eigenvalue Problem

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
1. Verfasser: Armentano, Diego
Format: Artikel
Sprache:eng
Schlagworte:
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
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Beschreibung
Zusammenfassung: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.
ISSN:1615-3375
1615-3383
DOI:10.1007/s10208-013-9185-5