Bounds for the Perron root of a nonnegative irreducible partitioned matrix
نویسندگان
چکیده
منابع مشابه
AN ALGORITHM FOR COMPUTING THE PERRON ROOT OF A NONNEGATIVE IRREDUCIBLE MATRIX by PRAKASH CHANCHANA
CHANCHAN, PRAKASH. An Algorithm for Computing the Perron Root of a Nonnegative Irreducible Matrix. (Under the direction of Carl D. Meyer.) We present a new algorithm for computing the Perron root of a nonnegative irreducible matrix. The algorithm is formulated by combining a reciprocal of the well known Collatz’s formula with a special inverse iteration algorithm discussed in [10, Linear Algebr...
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In this paper, we present some lower bounds for the Perron root of a symmetric nonnegative matrix, which are then applied to give the lower bounds of the Perron root of a general nonnegative matrix. These bounds improve the corresponding ones in [3] and [5]. Numerical examples are supplemented to illustrate the effectiveness of the presented bounds. Mathematics subject classification (2010): 15...
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As is well known, an irreducible nonnegative matrix possesses a uniquely determined Perron vector. As the main result of this paper we give a description of the set of Perron vectors of all the matrices contained in an irreducible nonnegative interval matrix A. This result is then applied to show that there exists a subset A∗ of A parameterized by n parameters (instead of n2 ones in the descrip...
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We propose an inverse iterative method for computing the Perron pair of an irreducible nonnegative third order tensor. The method involves the selection of a parameter θk in the kth iteration. For every positive starting vector, the method converges quadratically and is positivity preserving in the sense that the vectors approximating the Perron vector are strictly positive in each iteration. I...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1981
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1981.92.49