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2.1 General remarks
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I. Basic Tools of
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1.4 Sample Applications
2. Linear Algebra
Carl Gustav Jacob Jacobi, relaxed
Jacobi, in action
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- Huge subject; excellent textbooks
- Many library subroutines exist
- But: ``physical'' matrices often simple in structure
- Specific algorithms that may (may!) be self-programmed
- We will concentrate on
Relaxation Methods
But before that, some
General remarks
Subsections
2.1 General remarks
2.2 Exact Methods
2.2.1 Gauss Elimination and Back Substitution
2.2.2 Householder Transformation
2.2.3 LU Decomposition
2.2.4 Recursion Method
2.3 Iterative Methods
2.3.1 Iterative Improvement
2.3.2 Jacobi Relaxation
2.3.3 Gauss-Seidel Relaxation (GSR)
2.3.4 Successive Over-Relaxation (SOR)
2.3.5 Conjugate Gradient Method
2.4 Eigenvalues and Eigenvectors
2.4.1 Largest Eigenvalue and Related Eigenvector
2.4.2 Arbitrary Eigenvalue/-vector: Inverse Iteration
2.5 Sample Applications
2.5.1 Thermal Conduction in 1D
2.5.2 Potential Equation in 2D
Franz J. Vesely Oct 2005
See also:
"Computational Physics - An Introduction," Kluwer-Plenum 2001