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Recapitulation of Linear Algebra
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algorithm applied approximation property Assume assumption asymptotical basic iteration begin block-diagonal bound cg method Chebyshev coincides computation condition number contraction number convergence rate corresponding damped data_of-discretisation defined diagonal matrix discretisation eigenvalues eigenvector end end energy norm equivalent error estimate Exercise factor five-point function GauB-Seidel iteration GauB-Seidel method gradient method gridfunction Hackbusch 15 Hence Hermitian holds ILU decomposition implies index set inequality integer iteration matrix iterationparameter iterative method Jacobi method Lemma linear M-matrix matrix norm minimisation model problem multi-grid method obtains optimal parameters Poisson-model problem polynomial positive definite Proof Prove regular Remark representation respect Richardson iteration Richardson method satisfy scalar product Schur complement Schwarz iteration second normal form semi-iteration semi-iterative method SOR method spectral norm spectral radius SSOR subspace symmetric iteration Theorem third normal form triangular matrix two-grid vector weakly 2-cyclic xm+1 yields