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Article analysis:

The article provides an overview of recent advances and new challenges in the use of the Proper Generalized Decomposition (PGD) for solving multidimensional models. The authors provide a comprehensive review of the literature on this topic, citing numerous sources to support their claims. They also provide examples from various fields to illustrate how the PGD can be used to solve complex problems.

The article is well-written and provides a thorough overview of the topic at hand. However, it does not explore any potential risks associated with using the PGD or discuss any counterarguments that may exist against its use. Additionally, there is no discussion of possible biases or one-sided reporting that could be present in some sources cited by the authors. Furthermore, while the authors do mention some potential applications for the PGD, they do not provide any evidence to support their claims about its effectiveness or reliability in these contexts.

In conclusion, while this article provides a comprehensive overview of recent advances and new challenges in using the Proper Generalized Decomposition for solving multidimensional models, it does not explore any potential risks associated with its use or discuss any counterarguments that may exist against it. Additionally, there is no evidence provided to support its effectiveness or reliability in certain contexts mentioned by the authors.