We introduce a general criterion for blindly extracting a subset of sources in instantaneous mixtures. We derive the corresponding estimation equations and generalize them based on arbitrary nonlinear separating functions. A quasi-Newton algorithm for minimizing the criterion is presented, which reduces to the FastICA algorithm in the case when only one source is extracted. The asymptotic distr...

We first recall some properties of infinite tridiagonal matrices considered as matrix transformations in sequence spaces of the forms sξ , sξ , s (c) ξ , or lp(ξ). Then, we give some results on the finite section method for approximating a solution of an infinite linear system. Finally, using a quasi-Newton method, we construct a sequence that converges fast to a solution of an infinite linear ...

We describe a parallel method for unconstrained optimization based on the quasi-Newton descent method of Broyden, Fletcher, Goldfarb, and Shanno. Our algorithm is suitable for both single-instruction and multiple-instruction parallel architectures and has only linear memory requirements in the number of parameters used to ®t the data. We also present the results of numerical testing on both sin...

With the emergence of big data, there has been a growing interest in optimization routines that lead to faster convergence of Logistic Regression (LR). Among many optimization methods such as Gradient Descent, Quasi-Newton, Conjugate Gradient, etc., the Trust-region based truncated Newton method (TRON) algorithm has been shown to converge the fastest. The TRON algorithm also forms an important ...

We describe a quasi-linear algorithm for computing Igusa class polynomials of Jacobians of genus 2 curves via complex floating-point approximations of their roots. After providing an explicit treatment of the computations in quartic CM fields and their Galois closures, we pursue an approach due to Dupont for evaluating θconstants in quasi-linear time using Newton iterations on the Borchardt mea...

In this paper we proposed quasi-Newton and limited memory quasi-Newton methods for objective functions defined on Grassmann manifolds or a product of Grassmann manifolds. Specifically we defined bfgs and l-bfgs updates in local and global coordinates on Grassmann manifolds or a product of these. We proved that, when local coordinates are used, our bfgs updates on Grassmann manifolds share the s...

In this paper, we propose an approach to the multichannel blind deconvolution problem, based on the mutual information criterion and more generally on an appropriate system of estimating equations. Formulas for the quasiNewton algorithm and the asymptotic covariance matrix of the estimator are provided. More interesting results have been obtained in the pure deconvolution case. By a clever para...

In modeling and location analysis, most traditional fault location methods do not consider about the existence of practical nonlinear model in distribution network, such as the nonlinearity of load and grounding resistor. Hence, the adopted model can’t express the practical network, and the location results will lose practical meaning. Aiming at solving the question above, this paper proposes a...

In this paper we describe and analyze an algorithm for certain box constrained optimization problems that may have several local minima. A paradigm for these problems is one in which the function to be minimized is the sum of a simple function, such as a convex quadratic, and high frequency, low amplitude terms which cause local minima away from the global minimum of the simple function. Our me...