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Tests of energy conservation indicate that calculated solutions remain accurate for large numbers of time steps.
The proposed algorithms make forecast reconciliation feasible in business applications involving very large numbers of time series.
Furthermore, it was shown employing the configurations of small numbers of subcarriers, large numbers of time slots in GOFDM architecture preserves good spectral efficiency and, besides, yields PAPR even lower than single-carrier FDM scheme.
In order to increase the efficiency of these solvers, and to improve robustness, particularly for large numbers of time instances, the Generalized Minimal Residual Method (GMRES) is used to solve the implicit linear system over all coupled time instances.
This new GMRES/preconditioner combination is shown to be over an order of magnitude more efficient than the previous wave-number independent preconditioner for problems with large numbers of time instances and/or large reduced frequencies.
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A horizon graph allows for comparing and contrasting a large number of time series simultaneously.
The algorithm can be easily implemented on traditional databases or NoSQL databases to support a large number of time series.
This involves the use of hot-wire anemometry to capture a large number of time series of velocity throughout the wake of a model road passenger vehicle.
A particular challenge of the presented example is the need to simultaneously process a large number of time series (15 datasets with 12 sensors – 180 time series).
Typical simulation output data, produced by the simulation tool used for this work, has a large number of time steps, in the order of 103 106.
This constitutes the applicability of the procedure within an industrial application where a large number of time series is automatically forecasted in a flexible and data-driven way.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com