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In theoretical results, we have suggested a general filter regularization method of regularized solution (Section 2.2).
The image system for the method of regularized Stokeslets is developed and implemented.
The method of regularized stokeslets is extensively used in biological fluid dynamics due to its conceptual simplicity and meshlessness.
The coupling to the fluid is accomplished by the use of the method of regularized Stokeslets for the force and regularized rotlets for the torque.
Unfortunately, the use of standard implicit time integration methods for the method of regularized Stokeslets requires the solution of dense nonlinear systems of equations for many relevant problems.
The method of regularized Stokeslets is a numerical approach to approximating solutions of fluid structure interaction problems in the Stokes regime.
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Among many regularization methods, Tikhonov regularization is the most commonly used method of regularization which tries to obtain regularized solution to Ax = b by choosing x to fit data b in least-square sense, but penalize solutions of large norm [49, 50].
Remark The continuation method of the regularized parameter λ plays an important role in STP for find sparsest solutions of high quality.
Another multi-task learning method making use of regularized regression is the trace norm regularized method proposed by Chen et al. [43].
Here, we computed the partial correlations using the shrinkage estimation method, a form of regularized estimator of the covariance matrix and its inverse (Schafer and Strimmer, 2005 ).
Our approach is based on a variation of Ewald's summation method and the method of images for regularized and singular Stokeslets.
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