臺灣博碩士論文加值系統

本篇論文的主要目的是研究CG類迭代方法的性質，並且推廣至CR類迭代方法，接著探討GMR_star巢式迭代法的性質，再發展出GCR_star巢式迭代法，最後以Poisson方程式及Navier-Stokes方程式來作為測試的題目。

The primary object of this thesis is to investigate the properties of the CG family, and use the same way to develop the CR family. Next, we investigate the properties od nested iterative method, GMR_star, and develop the different nested iterative method, named GCR_star. Finally, we test these iterative methods by the Poisson equation and Navier-Stokes equation.

1 Introduction 8
2 The CG Family 9
2.1 The Conjugate Gradient(CG) Method...................9
2.2 The Bi-Conjugate Gradient(BCG) Method..............11
2.3 The Conjugate Gradient Squared(CGS) Method.........13
2.4 The Bi-Conjugate Gradient Stabilized(BCGs) Method..15
3 The Preconditioned CG Family 17
4 The CR Family 21
4.1 The Conjugate Residuak(CR) Method...................9
4.2 The Bi-Conjugate Residual(BCR) Method..............11
4.3 The Conjugate Residual Squared(CRS) Method.........13
4.4 The Bi-Conjugate Residual Stabilized(BCRs) Method..15
5 The Preconditioned CR Family 29
6 Nested Iterative Methods 34
6.1 The General Minimum Residual(GMRes) Method.........34
6.2 The GMR_star Method................................36
6.3 The GCR_star Method................................39
7 Basic Test 42
7.1 Two-Dimensional Poisson Problem....................42
7.2 Three-Dimensional Poisson Problem..................74
8 Application Test 103
9 Conclusions 108

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