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研究生:李雨蒨
研究生(外文):Yu-Chien Lee
論文名稱:解非對稱線性方成組之修正型MINRES方法
論文名稱(外文):The Modified MINRES Methods for Solving Large Sparse Nonsymmetric Linear System
指導教授:陳振遠陳振遠引用關係
指導教授(外文):Jen-Yuan Chen
學位類別:碩士
校院名稱:國立高雄師範大學
系所名稱:數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:中文
論文頁數:38
中文關鍵詞:論文
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  • 點閱點閱:198
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對於解對稱非正定線性方程組,SYMMLQ及MINRES方法效果良好。這篇論文提供另一種與SYMMLQ及MINRES等價的方法,並進而導出LAN/SYMMLQ及LAN/SYMMQR方法,他們可用於解非對稱線性方程組。
For solving systems of linear equations of Ax = b, where A is symmetric indefinite, the methods SYMMLQ and MINRES work fairly well. In this thesis we propose alternative methods which are equivalent to SYMMLQ and MINRES. Moreover, we generalized those methods to LAN/SYMMLQ and LAN/SYMMQR that are suitable for the nonsymmetric
linear systems.
1 Introduction

2 SYMMLQ and SYMMQR
2.1 Arnoldi process
2.2 SYMMLQ
2.3 SYMMQR

3 LQ-MINRES and QR-MINRES
3.1 LQ-MINRES
3.2 QR-MINRES
3.3 Relation between LQ-MINRES and QR-MINRES
3.4 A closer look at QR-MINRES and SYMMQR

4 Generalized MINRES Method
4.1 Generalized QR-MINRES Method
4.2 GMRES

5 The Difference between MMINRES and MGMRES
5.1 The Difference between MMINRES and MGMRES

6 Generalized SYMMLQ and SYMMQR
6.1 Modified SYMMLQ
6.2 Lanczos/SYMMLQ
6.3 Modified SYMMQR
6.4 LAN/SYMMQR

7 Conclusions
[1] J.-Y. Chen. Iterative Solution of Large Nonsymmetric Linear Systems. Report CNA-285, Center for Numerical Analysis, University of Texas at Austin, Austin, TX, 1997.

[2] Gene H. Golub and Charles F. Van Loan. Matrix Computations. the John Hopkins University Press, Baltimore and London, third edition, 1996.

[3] Cornelius Lanczos. An Iteration Method for the Solution of the Eigenvalue Problem of Linear Differential and Integral Operators. Journal of Research of the National Bureau of Standards, 45(4):255–282, 1950.

[4] C. C. Paige and M. A. Saunders. Solution of Sparse Indefinite Systems of Linear Equations. SIAM, J. Num. Anal., pages 617–629, 1975.

[5] Y. Saad and M. H. Schultz. GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems. SIAM, J. Scientific and Stat. Comp., 7:856–869, 1986.

[6] Yousef Saad. Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia PA., second edition, 2000.
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