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The solution is sought by applying a [[greedy algorithm]], usually the [[fixed point algorithm]], to the [[weak formulation]] of the problem.
For each iteration ''i'' of the algorithm, a ''mode'' of the solution is computed. Each mode consists of a set of numerical values of the functional products '''X<sub>1</sub>'''(''x''<sub>1</sub>), ..., '''X<sub>d</sub>'''(''x''<sub>d</sub>), which ''enrich'' the approximation of the solution
Unlike [[Principal Component Analysis|PCA]], PGD modes are not necessarily [[orthogonal]] to each other.
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