臺灣博碩士論文加值系統

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

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[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.

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