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=== Greedy algorithm ===
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. Note that due to the greedy nature of the algorithm, the term 'enrich' is used rather than 'improve'. The number of computed modes required to obtain an approximation of the solution below a certain error threshold depends on the stop criterium of the iterative algorithm. For the same reason and unlike [[Proper orthogonal decomposition|POD]], PGD modes are not necessarily [[orthogonal]] to each other.
== Features ==
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