1. On Perron–Frobenius property of matrices having some negative entries
- Author
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D. Noutsos
- Subjects
Perron–Frobenius theorem ,Perron–Frobenius splitting ,Numerical Analysis ,Pure mathematics ,Algebra and Number Theory ,Iterative method ,Linear system ,Nonnegative matrices ,Algebra ,symbols.namesake ,Matrix (mathematics) ,symbols ,Discrete Mathematics and Combinatorics ,Perron frobenius ,Geometry and Topology ,Nonnegative matrix ,Mathematics ,Frobenius theorem (real division algebras) - Abstract
We extend the theory of nonnegative matrices to the matrices that have some negative entries. We present and prove some properties which give us information, when a matrix possesses a Perron–Frobenius eigenpair. We apply also this theory by proposing the Perron–Frobenius splitting for the solution of the linear system Ax=b by classical iterative methods. Perron–Frobenius splittings constitute an extension of the well known regular splittings, weak regular splittings and nonnegative splittings. Convergence and comparison properties are given and proved.
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