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As can be noticed from the cost function convergence plots shown in Fig. 12, the HSDBC algorithm cost function has converged into the minimum value within approximately 25 iterations.
When compared with the logarithmic utility function, convergence to a local point was observed in significantly fewer cases.
The complete numerical procedure and details of assigning the numerical parameters are provided; convergence of the numerical method is demonstrated by conducting grid function convergence tests.
The method is implemented as a computer program and aspects of numerical problems regarding Green function convergence and the extraction of higher modes are discussed.
Fig. 11 Block diagram of the vehicle control system Fig. 12 Cost function convergence plot for BFA, SDA and HSDBC algorithms.
The approach introduced in this text produces fast Green function convergence throughout the spectrum on the basis of a certain "finite-differencing" approach and smooth windowing of the classical Green function lattice sum.
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The resulting Green-function convergence is super-algebraically fast away from Wood anomalies, and it reduces to an arbitrarily-high (user-prescribed) algebraic order of convergence at Wood anomalies.
Trapezoidal integration in time and centered differencing in space provide an accurate discretization, as demonstrated by comparisons with analytical and experimental results in one dimension, and via grid-function convergence tests in three dimensions.
The criteria are based on a combination of a point process, one-point and two-point probability functions; convergence of microstructure size; and equality of fiber radius distribution.
For these two types of functions, convergence is particularly common across the independent populations from the DOX, ERY, and C50 treatments (fig. 2, table 2, and supplementary table S4, Supplementary Material online).
A coherence function, a convergence function, and a convergence index are introduced to evaluate qualities of measured cross-correlation functions and associated cross-power spectra.
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