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Estimates of the upper and lower bounds of the non- negative matrix Perron root

Author: QianZuo
Tutor: HuangTingZhu
School: University of Electronic Science and Technology
Course: Computational Mathematics
Keywords: Non - negative matrix Perron root Estimate Irreducible Convert
CLC: O241.6
Type: Master's thesis
Year: 2007
Downloads: 93
Quote: 1
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Engineering calculations sometimes need to calculate the eigenvalues ??of large non - negative matrix , but more difficult to calculate the exact value . Therefore, can be estimated by some of the elements of the matrix or values ??, it is important to its eigenvalues ??. In this paper, irreducible non- negative matrix similarity transformation to generate different from the original matrix of rows and columns and to estimate the Perron root of the original matrix , which has been optimized for the upper and lower bounds of the Perron root . The text is divided into five chapters . The first chapter is the introduction introduces the research background and the problem to be solved . The second chapter describes the non- negative matrix Perron root theorem and development status . Introduces the history Perron root of several different calculation methods , the the famous Frobenius theorem . The third chapter describes a method to estimate the Perron root through three transformations : general similarity transformation estimate some special matrix Perron root symmetry transformation matrix trace Perron root of the estimated non - negative matrix diagonal transform estimated non- negative matrix Perron root . These three methods are improved on the basis of the previous , the improved method in the paper gives numerical examples to verify . Chapter IV presents a special matrix non the negative Persymmetric matrix , estimates of the Perron root of such a matrix can be obtained after it was generated by a symmetric matrix Perron root estimates . In this article gives the calculation of a sequence of non negative Persymmetric matrix lower bound . The fifth chapter discusses block non-negative irreducible matrix Perron root sector . Smaller than the order of matrix, the matrix of its sub- block utilization estimate the matrix of the original matrix Perron root . Block , the order of the matrix is greatly reduced this method is also a good estimate of the Perron root method .

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