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We present a method for performing sampling from a Boltzmann distribution of an ill-conditioned quadratic action. This method is based on heatbath thermalization along a set of conjugate directions, generated via a conjugate-gradient procedure. The resulting scheme outperforms local updates for matrices with very high condition number, since it avoids the slowing down of modes with lower eigenvalue, and has some advantages over the global heatbath approach, compared to which it is more stable and allows for more freedom in devising case-specific optimizations.
Fast computation of demagnetization curves is essential for the computational design of soft magnetic sensors or permanent magnet materials. We show that a sparse preconditioner for a nonlinear conjugate gradient energy minimizer can lead to a speed
Classical iterative algorithms for linear system solving and regression are brittle to the condition number of the data matrix. Even a semi-random adversary, constrained to only give additional consistent information, can arbitrarily hinder the resul
Conjugate gradient methods for energy minimization in micromagnetics are compared. When the step length in the line search is controlled, conjugate gradient techniques are a fast and reliable way to compute the hysteresis properties of permanent magn
In this short note, we present a new technique to accelerate the convergence of a FFT-based solver for numerical homogenization of complex periodic media proposed by Moulinec and Suquet in 1994. The approach proceeds from discretization of the govern
In this paper, we extend to the block case, the a posteriori bound showing superlinear convergence of Conjugate Gradients developed in [J. Comput. Applied Math., 48 (1993), pp. 327- 341], that is, we obtain similar bounds, but now for block Conjugate