The lower and upper bounds on Perron root of nonnegative irreducible matrices
نویسندگان
چکیده
منابع مشابه
Some Lower Bounds for the Perron Root of a Nonnegative Matrix
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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k=1 |ak|. Hardy’s inequality can be interpreted as the lp operator norm of the Cesàro matrix C, given by cj,k = 1/j, k ≤ j, and 0 otherwise, is bounded on lp and has norm ≤ p/(p − 1) (The norm is in fact p/(p − 1)). It is known that the Cesàro operator is not bounded below, or the converse of inequality (1.1) does not hold for any positive constant. However, if one assumes C acting only on non-...
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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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By a nonnegative matrix we mean a matrix whose entries are nonnegative real numbers. By positive matrix we mean a matrix all of whose entries are strictly positive real numbers. These notes give the core elements of the Perron-Frobenius theory of nonnegative matrices. This splits into three parts: (1) the primitive case (due to Perron) (2) the irreducible case (due to Frobenius) (3) the general...
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k=1 |ak| . Hardy’s inequality can be interpreted as the lp operator norm of the Cesàro matrix C, given by cj,k = 1/j, k ≤ j, and 0 otherwise, is bounded on l p and has norm ≤ p/(p − 1) (The norm is in fact p/(p − 1)). It is known that the Cesàro operator is not bounded below, or the converse of inequality (1.1) does not hold for any positive constant. However, if one assumes C acting only on no...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2008
ISSN: 0377-0427
DOI: 10.1016/j.cam.2007.06.034