1 Introduction
2 Tensors
2.1 Grid functions (\(V_{j}=\mathbb {R}^{n_{j}}\))
2.2 Functions (\(V_{j}=L^{2}(\Omega _{j})\))
2.3 Matrices (\(V_{j}=\mathbb {R}^{n_{j}\times m_{j}}\))
2.4 r-Term format (Canonical format)
2.5 Numerical tensor calculus
2.6 Truncation
2.7 Other tensor representations
3 Linear systems
3.1 Model problem: Laplace operator
3.2 Solution of linear systems
3.3 cg-Like methods
4 Multigrid approach
4.1 Grid hierarchy
4.2 Prolongation, restriction
4.3 Coarse-grid matrices
4.4 Smoothing
4.4.1 Richardson iteration
4.4.2 Jacobi iteration
4.5 Treatment of the coarsest grid
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either \(n_{j}^{(0)}=1,\)
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or \(n_{j}^{(0)}\) and d so small that also \(\prod _{j=1}^{d}n_{j}^{(0)}\) is sufficiently small.