Estimated That Of Non-negative Matrix Perron Roots Of The Upper And Lower Bounds

It is necessary to compute eigenvalues of matrices, but sometimes, it is verydifficult to obtain their exact eigenvalues. Therefore, it is particularly important tolocal the eigenvalues by some elements matrices. This paper, by using the theory ofPerron -Frobenius and some transformations, we obtain a few rows and columnswhich are difference from before. By these rows and columns, we can obtain betterestimation of the Perron roots. The text includes 5 chapters.In Chapter 1,we introduce the background of choosing this research and problemfor resolving.In Chapter 2, we introduce some related theories and developments about Perronroot. And it is foci on the introduction of Perron -Frobenius.In Chapter 3, three kinds of methods be introduced. These three kinds of methodsare all based on the formers' results., and examples are given in the text.In Chapter 4, a kind of special matrices—Persymmetric are given, the estimation ofthe Perron root of this kind of matrix can be pass to estimate the Perron root of asymmetry matrix.In Chapter 5, Bounds for the Perron Root of (Block) Nonnegative Matrices bediscussed. By partitioning into blocks, the order of the matrix be lower, so this methodis very useful.