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In this paper, we examine deflation-based algebraic multigrid methods for solving large systems of linear equations. Aggregation of the unknown terms is applied for coarsening, while deflation techniques are proposed for improving the rate of convergence. More specifically, the V-cycle strategy is adopted, in which, at each iteration, the solution is computed by initially decomposing it utilizing two complementary subspaces. The approximate solution is formed by combining the solution obtained using multigrids and deflation. In order to improve performance and convergence behavior, the proposed scheme was coupled with the Modified Generic Factored Approximate Sparse Inverse preconditioner. Furthermore, a parallel version of the multigrid scheme is proposed for multicore parallel systems, improving the performance of the techniques. Finally, characteristic model problems are solved to demonstrate the applicability of the proposed schemes, while numerical results are given.

The rise of deep learning algorithms has led many researchers to withdraw from using classic signal processing methods for sound generation. Deep learning models have achieved expressive voice synthesis, realistic sound textures, and musical notes from virtual instruments. However, the most suitable deep learning architecture is still under investigation. The choice of architecture is tightly coupled to the audio representations. A sound's original waveform can be too dense and rich for deep learning models to deal with efficientlyand complexity increases training time and computational cost. Also, it does not represent sound in the manner in which it is perceived. Therefore, in many cases, the raw audio has been transformed into a compressed and more meaningful form using upsampling, feature-extraction, or even by adopting a higher level illustration of the waveform. Furthermore, conditional on the form chosen, additional conditioning representations, different model architectures, and numerous metrics for evaluating the reconstructed sound have been investigated. This paper provides an overview of audio representations applied to sound synthesis using deep learning. Additionally, it presents the most significant methods for developing and evaluating a sound synthesis architecture using deep learning models, always depending on the audio representation.