In this article, we propose a relaxed algorithm for the split feasibility problem involving para-monotone equilibrium and convex optimization, which doesn't need the information of the operator norm. It improves t...
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ISBN:
(纸本)9781728146898
In this article, we propose a relaxed algorithm for the split feasibility problem involving para-monotone equilibrium and convex optimization, which doesn't need the information of the operator norm. It improves the feasibility and application range of the algorithm. And we prove the strong convergence of the algorithm.
We consider a variation of the well known problem of computing the unique solution to a nonsingular system Ax = b of n linear equations over a field K. The variation assumes that A has generic rank profile and require...
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ISBN:
(纸本)9781450334358
We consider a variation of the well known problem of computing the unique solution to a nonsingular system Ax = b of n linear equations over a field K. The variation assumes that A has generic rank profile and requires as output not only the single solution vector A(-1) b is an element of K-nx1, but rather the solution to all leading principle subsystems. Most importantly, the rows of the augmented system [A parallel to b] are given one at a time from first to last, and as soon as the next row is given the solution to the next leading principal subsystem should be produced. We call this problem ONLINESYSTEM. The obvious iterative algorithm for ONLINESYSTEM has a cost in terms of field operations that is cubic in the dimension of A. In this paper we introduce a relaxed representation for the inverse and show how to obtain an algorithm for ONLINESYSTEM that allows us to incorporate matrix multiplication. As an application we show how to introduce fast matrix multiplication into the inherently iterative algorithm for row rank profile computation presented previously by the authors.
In this paper, an absorbing Fictitious Boundary Condition (FBC) is presented to generate an iterative Domain Decomposition Method (DDM) for analyzing waveguide *** relaxed algorithm is introduced to improve the iterat...
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In this paper, an absorbing Fictitious Boundary Condition (FBC) is presented to generate an iterative Domain Decomposition Method (DDM) for analyzing waveguide *** relaxed algorithm is introduced to improve the iterative convergence. And the matrix equations are solved using the multifrontal algorithm. The resulting CPU time is greatly ***, a number of numerical examples are given to illustrate its accuracy and efficiency.
In this paper we present several relaxed inexact projection methods for the split feasibility problem (SFP). Each iteration of the first proposed algorithm consists of a projection onto a halfspace containing the give...
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In this paper we present several relaxed inexact projection methods for the split feasibility problem (SFP). Each iteration of the first proposed algorithm consists of a projection onto a halfspace containing the given closed convex set. The algorithm can be implemented easily and its global convergence to the solution can be established under suitable conditions. Moreover, we present some modifications of the relaxed inexact projection method with constant stepsize by adopting Armijo-like search. We furthermore present a variable-step relaxed inexact projection method which does not require the computation of the matrix inverses and the largest eigenvalue of the matrix A(T)A, and the objective function can decrease sufficiently at each iteration. We show convergence of these modified algorithms under mild conditions. Finally, we perform some numerical experiments, which show the behavior of the algorithms proposed. (C) 2011 Published by Elsevier Inc.
In this paper, we present a new lifting algorithm for triangular sets over general p-adic rings. Our contribution is to give, for any p-adic triangular set, a shifted algorithm of which the triangular set is a fixed p...
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In this paper, we present a new lifting algorithm for triangular sets over general p-adic rings. Our contribution is to give, for any p-adic triangular set, a shifted algorithm of which the triangular set is a fixed point. Then we can apply the relaxed recursive p-adic framework and deduce a relaxed lifting algorithm for this triangular set. We compare our algorithm to the existing technique and report on implementations inside the c++ library GEOMSOLVEX of MATHEMAGIX (van der Hoeven et al., 2002). Our new relaxed algorithm is competithie and compare favorably on some examples. (C) 2014 Elsevier Ltd. All rights reserved.
In this paper, we propose four alternated inertial algorithms with self-adaptive stepsize to address the split equality equilibrium problem (SEEP) in real Hilbert spaces, without the need for any prior knowledge of th...
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In this paper, we propose four alternated inertial algorithms with self-adaptive stepsize to address the split equality equilibrium problem (SEEP) in real Hilbert spaces, without the need for any prior knowledge of the operator norm. Moreover, these algorithms adopt the convex subset form by a sequence of closed balls rather than half-spaces, and it is simple to calculate the projections onto these sets. Under some proper assumptions, we demonstrate weak and strong convergence theorems of our algorithms, particularly strong convergence towards the minimum-norm solution of the SEEP. As application, we will utilize our results to study the split equality variational inequality problem. Finally, we provide a numerical example to illustrate the effectiveness of the proposed algorithms.
Community detection in networks including singed edges is a primary challenge that has already attracted substantial attention. In this paper, we show that this task could be reformulated as a combinatorial optimizati...
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Community detection in networks including singed edges is a primary challenge that has already attracted substantial attention. In this paper, we show that this task could be reformulated as a combinatorial optimization concerning the trace of the signed modularity matrix. Keeping the orthogonal and nonnegative constraints in the relaxation, we propose a multiplicative update rule, named the SMON algorithm, which results in a solution that is a close approximation to the genuine community indication matrix. In addition, the rows of the solution can be referred to as the probabilities of corresponding vertex falling into each community, which can help us to discover the overlapping community structure of the network and identify vertices that reside on the watersheds between different communities. Experimental results on real-life social networks as well as synthetic signed networks verify that our method is effective and superior to the existing approaches.
This paper focuses on online (or relaxed) algorithms for the multiplication of power series over a field and their complexity analysis. We propose a new online algorithm for the multiplication using middle and short p...
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This paper focuses on online (or relaxed) algorithms for the multiplication of power series over a field and their complexity analysis. We propose a new online algorithm for the multiplication using middle and short products of polynomials as building blocks, and we give the first precise analysis of the arithmetic complexity of various online multiplications. Our algorithm is faster than Fischer and Stockmeyer's by a constant factor;this is confirmed by experimental results. (C) 2015 Elsevier Ltd. All rights reserved.
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