Complexity results for some eigenvector problems

We consider the computation of eigenvectors over the integers, where each component x i satisfies for an integer b. We address various problems in this context, and analyze their computational complexity. We find that different problems are complete for the complexity classes Applying the results, f...

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Bibliographic Details
Published in:International journal of computer mathematics Vol. 76; no. 1; pp. 59 - 74
Main Authors: Eiter, Thomas, Gottlob, Georg
Format: Journal Article
Language:English
Published: Abingdon Gordon and Breach Science Publishers 2000
Taylor and Francis
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Calculus of variations and optimal control
Combinatorial optimization
Computer science; control theory; systems
Eigenvectors
Exact sciences and technology
F.2.1.[Analysis of Algorithms and Problem Complexity]
G.1.6[Numerical Analysis]
Logic and foundations
Mathematical analysis
Mathematical logic, foundations, set theory
Mathematical programming
Mathematics
Numerical Algorthims and Problems - computation on matrices
Operational research and scientific management
Operational research. Management science
Optimization - integer programming
Problem complexity
Recursion theory
Sciences and techniques of general use
Theoretical computing
Eigenvector
NP hard problem
Eigenvalue problem
Satisfiability problem
Combinatorial optimization
Computational complexity
Mathematical programming
ISSN:0020-7160, 1029-0265
Online Access:Get full text
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Summary:We consider the computation of eigenvectors over the integers, where each component x i satisfies for an integer b. We address various problems in this context, and analyze their computational complexity. We find that different problems are complete for the complexity classes Applying the results, finding bounded solutions of a Diophantine equation is shown to be intractable.
ISSN:0020-7160
1029-0265
DOI:10.1080/00207160008805009