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A method for computing the Perron root for primitive matrices.
- Source :
- Numerical Linear Algebra with Applications; Jan2021, Vol. 28 Issue 1, p1-14, 14p
- Publication Year :
- 2021
-
Abstract
- Summary: Following the Perron theorem, the spectral radius of a primitive matrix is a simple eigenvalue. It is shown that for a primitive matrix A, there is a positive rank one matrix X such that B = A ∘ X, where ∘ denotes the Hadamard product of matrices, and such that the row (column) sums of matrix B are the same and equal to the Perron root. An iterative algorithm is presented to obtain matrix B without an explicit knowledge of X. The convergence rate of this algorithm is similar to that of the power method but it uses less computational load. A byproduct of the proposed algorithm is a new method for calculating the first eigenvector. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10705325
- Volume :
- 28
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Numerical Linear Algebra with Applications
- Publication Type :
- Academic Journal
- Accession number :
- 147336866
- Full Text :
- https://doi.org/10.1002/nla.2340