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For comparison, we also implemented a gradient search algorithm according to Section 2.2, where we chose the gradient finding step size to be δ=10 in general and δ=2 for LCC settings close to the optimum LCC setting point.
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Using an adjoint equation we implement a gradient algorithm for the minimization of the objective function.
Later on, a concept of impurity distributed homojunction is demonstrated to enhance charge separation by implementing a gradient in the dopant concentration.
A baseline separation of 11 intact proteins was obtained within 20 min by implementing a gradient across a limited RP composition window in the second dimension.
We implement a steepest gradient descent method for parameter inference using the estimated gradient information in a MATLAB software package http://cbcl.ics.uci.edu/sgd.uci.edu/sgd
The method was implemented using a gradient correlation similarity metric and stochastic derivative-free optimization on a GPU.
The inverse problem relies on a classic local optimization approach implemented with a gradient method.
The statistical independence is usually represented by negentropy or kurtosis that is fourth-order cumulant, and maximization of statistical independence is implemented in a gradient algorithm or fixed-point algorithm.
These rules can be implemented using a gradient descent algorithm with an appropriate choice of the step size and are estimated for each scalar parameter Z by expressing the partial derivatives of the objective function ∂D ∂Z as the division between two positive terms ∂D ∂Z − and ∂D ∂Z + : Z = Z ⊙ ∂D ∂Z − ∂D ∂Z + (10).
To solve the corresponding linear system efficiently on the GPU, we implement a conjugate gradient method preconditioned with a geometry-informed algebraic multigrid (AMG) method preconditioner.
Although the distance field, as tested herein, also implements an averaged gradient on the block's boundary, it does not affect the convergence at least in this example.
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