Algorithms2015, 8(4), 799-809; doi:10.3390/a8040799 - published 25 September 2015 Show/Hide Abstract
Abstract: The sign least mean square with reweighted L1-norm constraint (SLMS-RL1) algorithm is an attractive sparse channel estimation method among Gaussian mixture model (GMM) based algorithms for use in impulsive noise environments. The channel sparsity can be exploited by SLMS-RL1 algorithm based on appropriate reweighted factor, which is one of key parameters to adjust the sparse constraint for SLMS-RL1 algorithm. However, to the best of the authors’ knowledge, a reweighted factor selection scheme has not been developed. This paper proposes a Monte-Carlo (MC) based reweighted factor selection method to further strengthen the performance of SLMS-RL1 algorithm. To validate the performance of SLMS-RL1 using the proposed reweighted factor, simulations results are provided to demonstrate that convergence speed can be reduced by increasing the channel sparsity, while the steady-state MSE performance only slightly changes with different GMM impulsive-noise strengths.
Algorithms2015, 8(3), 786-798; doi:10.3390/a8030786 - published 22 September 2015 Show/Hide Abstract
Abstract: In this paper, a general family of n-point Newton type iterative methods for solving nonlinear equations is constructed by using direct Hermite interpolation. The order of convergence of the new n-point iterative methods without memory is 2n requiring the evaluations of n functions and one first-order derivative in per full iteration, which implies that this family is optimal according to Kung and Traub’s conjecture (1974). Its error equations and asymptotic convergence constants are obtained. The n-point iterative methods with memory are obtained by using a self-accelerating parameter, which achieve much faster convergence than the corresponding n-point methods without memory. The increase of convergence order is attained without any additional calculations so that the n-point Newton type iterative methods with memory possess a very high computational efficiency. Numerical examples are demonstrated to confirm theoretical results.
Algorithms2015, 8(3), 774-785; doi:10.3390/a8030774 - published 15 September 2015 Show/Hide Abstract
Abstract: In this paper we investigate some parallel variants of Broyden’s method and, for the basic variant, we present its convergence properties. The main result is that the behavior of the considered parallel Broyden’s variants is comparable with the classical parallel Newton method, and significantly better than the parallel Cimmino method, both for linear and nonlinear cases. The considered variants are also compared with two more recently proposed parallel Broyden’s method. Some numerical experiments are presented to illustrate the advantages and limits of the proposed algorithms.
Algorithms2015, 8(3), 754-773; doi:10.3390/a8030754 - published 10 September 2015 Show/Hide Abstract
Abstract: DNA fragment assembly represents an important challenge to the development of efficient and practical algorithms due to the large number of elements to be assembled. In this study, we present some graph theoretical linear time algorithms to solve the problem. To achieve linear time complexity, a heap with constant time operations was developed, for the special case where the edge weights are integers and do not depend on the problem size. The experiments presented show that modified classical graph theoretical algorithms can solve the DNA fragment assembly problem efficiently.
Algorithms2015, 8(3), 743-753; doi:10.3390/a8030743 - published 10 September 2015 Show/Hide Abstract
Abstract: This paper considers identifying the multiple input single output finite impulse response (MISO-FIR) systems with unknown time delays and orders. Generally, parameters, orders and time delays of an MISO system are separately identified from different algorithms. In this paper, we aim to perform the model identification and time delay estimation simultaneously from a limited number of observations. For an MISO-FIR system with many inputs and unknown input time delays, the corresponding identification model contains a large number of parameters, requiring a great number of observations for identification and leading to a heavy computational burden. Inspired by the compressed sensing (CS) recovery theory, a threshold orthogonal matching pursuit algorithm (TH-OMP) is presented to simultaneously identify the parameters, the orders and the time delays of the MISO-FIR systems. The proposed algorithm requires only a small number of sampled data compared to the conventional identification methods, such as the least squares method. The effectiveness of the proposed algorithm is verified by simulation results.
Algorithms2015, 8(3), 723-742; doi:10.3390/a8030723 - published 28 August 2015 Show/Hide Abstract
Abstract: In this contribution a comparative study of modern heuristics on the school timetabling problem is presented. More precisely, we investigate the application of two population-based algorithms, namely a Particle Swarm Optimization (PSO) and an Artificial Fish Swarm (AFS), on the high school timetabling problem. In order to demonstrate their efficiency and performance, experiments with real-world input data have been performed. Both algorithms proposed manage to create feasible and efficient high school timetables, thus fulfilling adequately the timetabling needs of the respective high schools. Computational results demonstrate that both algorithms manage to reach efficient solutions, most of the times better than existing approaches applied to the same school timetabling input instances using the same evaluation criteria.