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The local factor and the adaptable variance solution are useful to detect changes in the scratch thickness.
It is known that this exaggerative effect on the outliers is reduced with the use of l1-norm and hence, its minimization could be a meliorative strategy w.r.t the minimum variance solution, in that the error on the outliers are less penalized [11].
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The minimum-variance solution can be obtained using the stochastic gradient algorithm {Q}^{m+1}={Q}^m-{mu}^m{f}_{mathbf{Q}}^{hboxleft({Q}^mright)left[varDelta d-fleft({Q}^mright)right], (8).
The primary contribution of this paper is to present a novel approach to track mean as well as variance of a set of policies in a dynamic stochastic programming model and using the mean-variance solutions in a simple heuristic for creating efficient risk-reward frontiers.
For the second moment computation, an efficient low-rank approximation of the pivoted Cholesky decomposition is proposed to compute the two-point correlation function to approximate the variance of solutions.
The aim of this paper is to compute the mean field and variance of solutions to three-dimensional Maxwell's equations with random interfaces via shape calculus and pivoted low-rank approximation.
Moreover, to achieve statistically reliable results, each algorithm was run 100 times on each problem and the best, the average, and the variance of solutions were reported in Table 5.
We show how the variance of the solution can be manipulated by the boundary conditions, while keeping the mean value of the solution unaffected.
Figure 11 Variance of the solution at (pmb{t=4mbox{ h}}).
Figure 5 Variance of the solution at (pmb{t=39mbox{ s}}).
The expectation and variance of the solution are derived.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com