Topic
Rate of convergence
About: Rate of convergence is a research topic. Over the lifetime, 31257 publications have been published within this topic receiving 795334 citations. The topic is also known as: convergence rate.
Papers published on a yearly basis
Papers
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TL;DR: The concept of a canonical mask for a given matrix mask is introduced and by investigating several properties of the initial function vectors in a vector cascade algorithm, a relatively unified approach is taken to study several questions such as convergence, rate of convergence and error estimate for a perturbed mask of avector cascade algorithm in a Sobolev space.
164 citations
TL;DR: This paper studies the statistical behavior of an affine combination of the outputs of two least-mean-square adaptive filters that simultaneously adapt using the same white Gaussian inputs to obtain an LMS adaptive filter with fast convergence and small steady-state mean-square deviation (MSD).
Abstract: This paper studies the statistical behavior of an affine combination of the outputs of two least mean-square (LMS) adaptive filters that simultaneously adapt using the same white Gaussian inputs. The purpose of the combination is to obtain an LMS adaptive filter with fast convergence and small steady-state mean-square deviation (MSD). The linear combination studied is a generalization of the convex combination, in which the combination factor lambda(n) is restricted to the interval (0,1). The viewpoint is taken that each of the two filters produces dependent estimates of the unknown channel. Thus, there exists a sequence of optimal affine combining coefficients which minimizes the mean-square error (MSE). First, the optimal unrealizable affine combiner is studied and provides the best possible performance for this class. Then two new schemes are proposed for practical applications. The mean-square performances are analyzed and validated by Monte Carlo simulations. With proper design, the two practical schemes yield an overall MSD that is usually less than the MSDs of either filter.
164 citations
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TL;DR: This work gives a simple proof that the Frank-Wolfe algorithm obtains a stationary point at a rate of $O(1/\sqrt{t})$ on non-convex objectives with a Lipschitz continuous gradient.
Abstract: We give a simple proof that the Frank-Wolfe algorithm obtains a stationary point at a rate of $O(1/\sqrt{t})$ on non-convex objectives with a Lipschitz continuous gradient. Our analysis is affine invariant and is the first, to the best of our knowledge, giving a similar rate to what was already proven for projected gradient methods (though on slightly different measures of stationarity).
164 citations
TL;DR: In this paper, a new adaptive switching learning control approach, calledadapt switching learning PD control (ASL-PD), is proposed for trajectory tracking of robot manipulators in an iterative operation mode and achieves the asymptotical convergence based on the Lyapunovs method.
163 citations
TL;DR: A novel matrix recurrence is introduced yielding a new spectral analysis of the local transient convergence behavior of the alternating direction method of multipliers (ADMM), for the particular case of a quadratic program or a linear program.
Abstract: We introduce a novel matrix recurrence yielding a new spectral analysis of the local transient convergence behavior of the alternating direction method of multipliers (ADMM), for the particular case of a quadratic program or a linear program. We identify a particular combination of vector iterates whose convergence can be analyzed via a spectral analysis. The theory predicts that ADMM should go through up to four convergence regimes, such as constant step convergence or linear convergence, ending with the latter when close enough to the optimal solution if the optimal solution is unique and satisfies strict complementarity.
163 citations