Dissertation > Excellent graduate degree dissertation topics show

Study on the Eigenvalues and Singular Value of Matrices and the Spectral Radius of Non-Negative Matrices

Author: ZhangCong
Tutor: WuJunLiang
School: Chongqing University
Course: Operational Research and Cybernetics
Keywords: eigenvalues the smallest singular value non-negative matrix spectral radius
CLC: O151.21
Type: Master's thesis
Year: 2011
Downloads: 66
Quote: 0
Read: Download Dissertation

Abstract


Matrix calculations and matrix analysis have wide application in economics, computational mathematics, computer graphics and image analysis. This paper studies the smallest singular value of matrices, the spectral radius of non-negative matrix and the existence of matrix eigenvalues. The thesis consists of five chapters.The first chapter mainly provides the development of matrix and the numerical characteristics of matrix. Then we introduce a special matrix—nonnegative matrix, we tell significance of the Perron root.The second chapter gives an overview of the smallest singular value and gives one good results of the smallest singular value by some nature of M matrix and Blocks matrix, this At last, we give an example about this.The third chapter gives some spectral radius of one special matrix—non-negative matrix. In this chapter we mainly gives some the below sequences by the theory of the iteration matrix and blocks matrix.The forth chapter gives an overview of matrix eigenvalues and introduces some scholars study about the existing regional of matrix eigenvalues the characteristic value exist in the domain (by the multiple plates to a disc), and the scholars gives some good results in recent years.The last chapter gives summary of all the content and illustrates the research content of this paper.

Related Dissertations

  1. Research of Sparse Represention Based Face Recognition Algorithm,TP391.41
  2. Judgement for Nonsingular H-matrices and Estimation for the Eigenvalues of Matrices,O151.21
  3. Inviscid Limits for the Navier-Stokes Equations in 3D Domains with Friction Boundary Conditions,O35
  4. Positive Solutions of Nonlinear Singular Problems and non - trivial solution,O175.8
  5. Trace Formula for the System of Equation about Sturm-Liouville Eigenvalue Problem with Two Different Boundary Conditions,O175.8
  6. Study on Characteristics of Inter-area Low Frequency Power Oscillation in Interconnected Power Grid,TM712
  7. Eigenvalues and Structural Parameters of Bicyclic Graphs,O157.5
  8. Iterative Algorithms for Saddle Point Problems,O241.6
  9. Application of Numerical Methods Based on Artificial Glowworm Optimization Algorithm,O241
  10. The Study of Several Force Gradient Symplectic Algorithms,O241
  11. Linearized equations of the two-particle Boltzmann integral operator eigenvalue problem and two particle Boltzmann H- Theorem,O35
  12. Eigenvalue Problems of Nonnegative Tensors,O183.2
  13. Discontinuous Sturm-Liouville Operator with Boundary Condition Depending on Spectral Parameter and Indefinite Weight Function,O177
  14. Laplacian Spectral Radii of Bipartite Graphs with Given Order and Size,O157.5
  15. Other Eigenvalues of the M/M/1 Queueing Model with Exceptional Service Time for the First Customer in Each Busy Period,O226
  16. Some Graphic Characters of the Laplacian Spectrum in Tricyclic Graphs,O157.5
  17. Chamber blasting rock fragmentation prediction,TD235.34
  18. Estimates of the Bounds of Spectral Radius and the Smallest Singular Value of LDD-matrix,O151.21
  19. Estimates for Eigenvalues of Laplacian Operator with Any Order,O177
  20. Continuous Dependence of Eigenvalues to Jacobi Operators,O177

CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Theory of algebraic equations,linear algebra > Linear Algebra > Matrix theory
© 2012 www.DissertationTopic.Net  Mobile