Dissertation > Excellent graduate degree dissertation topics show

Generalized Inverse A_ (T, S) ~ (2) , said the application and testing of the approximation , iterative method and Drazin inverse

Author: ZhangXiangYun
Tutor: ChenGuoLiang
School: East China Normal University
Course: Computational Mathematics
Keywords: Linear operator Banach space A (T S) 2 Inverse Moore-Penrose generalized inverse Drazin inverse Group inverse Representation and Approximation Iterative method Markov chain Test matrix
CLC: O241
Type: Master's thesis
Year: 2004
Downloads: 90
Quote: 1
Read: Download Dissertation

Abstract


Linear representation of the generalized inverse calculation is very important in the theory of generalized inverse research topics in the field of theoretical research attention has been paid or are in actual use in (see [1,2,3,9,10 11,12,13,17,21,23,30]). Many scholars, Adi Ben in Israel, K.Kato, MZNashed YYTseng J.Ding, Kuang Jiao Hoon, Guo-Liang Chen, Xue to front, Joe tri-n-and Wei Yimin and other people in the Hilbert space and Banach space of linear operator of Moore-Penrose generalized inverse, Drazin inverse and group inverse of the existence, nature, approximation, perturbation theory, applications and computing theory has done a lot of work to get some good results. But the result is still relatively fragmented, in stark contrast with the case of a matrix. The first part of this article operator A T, S (2) inverse based on the establishment of a the common generalized inverse unified representation theory and iterative format, we have given a Banach the space operator A. T S (2) inverse limit of the Neumann series and integral representation, as well as the approximate error estimates. Based on the various representations, we construct a calculation the A T S (2) the inverse Several iterative schemes, such as: Neumann series-type iterative method, Newton iterative method, super power iteration and iterative method based on the interpolation function, and discuss the convergence conditions and the speed of convergence. this technique is used in the calculation of the the MP inverse and Drazin inverse. We generalize this technique and apply it to the matrix A T S (2) inverse of calculation, so that the Neumann series iterative method convergence speed by an order up to second order, the convergence rate of Iteration order p to 2 p second-order calculation just doubled. The block multiplication techniques discussed in this article has been faster convergent sequence, the computation still [38] given in the same order, the analysis shows that our promotional techniques more suitable for parallel computing. Finally, we construct an the Markov chain unconditional convergence and accelerate the convergence techniques used in which, we also carried out numerical experiments. How to evaluate the pros and cons of the algorithm has been the actual calculation of the workers concerned about the problem, most people in the past, in theory, computational algorithm, the convergence rate and other indicators, and less care about the performance of the algorithm in the actual calculation. test matrix Drazin inverse calculation method for several common tests listed in the test report. We found that for the calculation of the group inverse indicators power zero solution, this paper constructed QAQ Neumann series iterative method has better performance, and can handle large-scale matrix; the Faddeev-type calculation of low-level matrix, especially effective, but can not handle more than 50 orders of the matrix; Newton iteration Iteration good effects of low-level matrix, also can not be used for more than 50 orders of the matrix. For the calculation of the Drazin inverse (excluding group inverse), the test results have been disappointing, the indicator increases greatly increase the difficulty of the calculation.

Related Dissertations

  1. The Research on Ship Imaging Algorithm under the Sea Clutter Background,TN958
  2. Modeling of Sea Clutter and Effect of Sea Clutter on Isar Imaging,TN957.54
  3. ISAR Imaging Simulation of Space Targets and Target Recognition Based on ISAR Images,TN957.52
  4. Design of Weapon Detection Device Control System,TP183
  5. Based on statistics of the lognormal distribution heteroscedasticity model inferred,O212.1
  6. Adaptive Homopoty Method Using Conjugate Gradient Algorithm for Inversion of Two-dimensional Wave Equation with Well Log Constraint,P631.81
  7. Identification of the Causal Organism of Soybean Bacterial Spots and Two Type Ⅲ Secreted Effectors’s Clone and Functional Analysis,S435.651
  8. High School Level of Understanding of Inverse Function and the Law of Development Research,G633.6
  9. Cao Mine Ventilation Optimization of multi-regional,TD724
  10. Virtual Human Motion Simulation,R318.0
  11. Researches on Urban Rail Transportation Operation Management System Test and Evaluation Method,TP311.52
  12. Detection and Tracking of Moving Object in Complex Background,TP391.41
  13. Study on Medical Image Preprocessing and Visualiztion Application Technology in IMRT Invrse Planning System,TP391.41
  14. Research of Virtual Machining Technology of Laser Processing Robot with Multi-degree of Freedom,TP242
  15. Research on Song Emotion Classification Methods Combining Music Content and Lyrics,TP391.3
  16. Study of Electromagnetic Tomography Image Reconstruction Based on Finite Element and Genetic Algorithm,TM15
  17. Application of the Fractional Fourier Transform to ISAR Maneuvering Target Imaging,TN957.52
  18. Electrical Impedance Tomography numerical solution of the problem in some studies,O441.4
  19. Traffic Prediction Model Based on Wavelet and Markov,TP393.06
  20. Research on Data Rectification Methods for Process Industry,TP274
  21. Research on Adaptive Inverse Control for the Hysteresis and Creep Characteristics of IPMC,TP273.2

CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis
© 2012 www.DissertationTopic.Net  Mobile