數值分析
Fall 2006
*Reading
**Home Work
***Programming
Lecture 1. 1D Poisson's Equation and Finite Difference Method (p. 1)
Lecture 2. Gaussian
Elimination 1*** (pdf*) Ax=b (p. 4)
Lecture 3. Jacobi’s Method
(JM)*** (pdf*) Ax=b (p. 8)
Templates
for the Solution of Linear Systems (pdf)
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Ferng’s Lecture
Notes on Iterative Methods*
Lecture 4. Gauss-Seidel Method (GS)*** Ax=b (p. 13)
Lecture 5. The
Successive Overrelaxation Method (SOR)*** Ax=b (p. 16)
Lecture 6. The Symmetric Successive Overrelaxation Method (SSOR)*** Ax=b (p. 18)
Lecture 7. Conjugate
Gradient Method (CG)* (CG.pdf*) Ax=b (p. 22)
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An
Introduction to the Conjugate Gradient Method Without
the Agonizing Pain by Jonathan Richard Shewchuk.
Lecture 8. Finite
Element Method for 1D Poisson’s Problem* Ax=b (p. 39-49)
Lecture 9. 2D and
3D Poisson’s Equation
Topics
Covered Above
I.
Numerical Methods
for PDEs
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Finite Element Method
(FEM) (pdf*)
II.
Numerical Methods
for Solving Ax=b
IV.
Mathematical
Sciences Digital Library
V.
Appendices