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Memory Cards — Chapter 5
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Jacobi
Jacobi is simple and parallelizable, but convergence can be slow.
Preconditioning
A preconditioner changes the problem so that the iteration converges faster while preserving the solution.
SOR
SOR depends critically on the relaxation parameter \(\omega\).
Gauss--Seidel
Gauss--Seidel uses new components immediately and often converges faster than Jacobi.
Stationary iteration
Convergence of \(x^{(k+1)}=Bx^{(k)}+c\) depends on \(\rho(B)<1\).
Iterative method
Iterative solvers build a sequence \(x^{(k)}\). They are essential for large sparse systems.