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Another example is data compression when original data is transformed into a space of lower dimension.
Combined with the Galerkin projection, POD is a tool for generation of reduced models of lower dimension.
The computation of the remaining states of the system requires matrices of lower dimension and thus the method is less susceptible to ill-conditioning.
The array of processing elements termed as the PE array is allocated to the indentified computational sub-space which is strictly of lower dimension than the n-D problem space.
We show that every spectral pair can be factored (in the sense of Cartesian products) as a product of two pairs of lower dimension where the first factor is a fundamental domain, and the second a simple factor.
In principle, this could be accomplished by solving a Riemann problem for the full system, but some ideas related to barotropic baroclinic time splitting can be used to reduce the Riemann problem to a much simpler system of lower dimension.
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Non-manifold geometric modeling allows the representation of multiregion objects, of internal or dangling structures, and of lower dimensions degenerated parts.
Sufficient conditions in the form of two algebraic Riccati equations (AREs) and an upper bound explicitly characterize an H∞ controller of lower dimensions.
Moreover, GSL can be applied to large composite structures without knowing the material performances, but by testing prototypes of lower dimensions.
This approach, based on the singular perturbation theory, decomposes the original system of the observer error dynamics into separate slow and fast subsystems of lower dimensions and permits a simple design and sequential determination of the observer gains.
The objective of VQ is to statistically preserve the topological relationships existing in a data set and to project the data to a lattice of lower dimensions, for visualization, compression, storage, or transmission purposes.
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