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Journal articles on the topic 'Linear Algorithms'

Author: Grafiati

Published: 4 June 2021

Last updated: 18 February 2022

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1

Patel, Roshni V., and Jignesh S. Patel. "Optimization of Linear Equations using Genetic Algorithms." Indian Journal of Applied Research 2, no. 3 (October 1, 2011): 56–58. http://dx.doi.org/10.15373/2249555x/dec2012/19.

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2

Eaves, B. Curtis, and Uriel G. Rothblum. "Linear Problems and Linear Algorithms." Journal of Symbolic Computation 20, no. 2 (August 1995): 207–14. http://dx.doi.org/10.1006/jsco.1995.1047.

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3

LAWLOR, DAVID, YANG WANG, and ANDREW CHRISTLIEB. "ADAPTIVE SUB-LINEAR TIME FOURIER ALGORITHMS." Advances in Adaptive Data Analysis 05, no. 01 (January 2013): 1350003. http://dx.doi.org/10.1142/s1793536913500039.

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We present a new deterministic algorithm for the sparse Fourier transform problem, in which we seek to identify k ≪ N significant Fourier coefficients from a signal of bandwidth N. Previous deterministic algorithms exhibit quadratic runtime scaling, while our algorithm scales linearly with k in the average case. Underlying our algorithm are a few simple observations relating the Fourier coefficients of time-shifted samples to unshifted samples of the input function. This allows us to detect when aliasing between two or more frequencies has occurred, as well as to determine the value of unaliased frequencies. We show that empirically our algorithm is orders of magnitude faster than competing algorithms.

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4

Galperin, E. A. "Linear time algorithms for linear programming." Computers & Mathematics with Applications 37, no. 4-5 (February 1999): 199–208. http://dx.doi.org/10.1016/s0898-1221(99)00069-3.

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5

Askar, S. S., and A. A. Karawia. "On Solving Pentadiagonal Linear Systems via Transformations." Mathematical Problems in Engineering 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/232456.

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Many authors have studied numerical algorithms for solving the linear systems of pentadiagonal type. The well-known fast pentadiagonal system solver algorithm is an example of such algorithms. The current paper describes new numerical and symbolic algorithms for solving pentadiagonal linear systems via transformations. The proposed algorithms generalize the algorithms presented in El-Mikkawy and Atlan, 2014. Our symbolic algorithms remove the cases where the numerical algorithms fail. The computational cost of our algorithms is better than those algorithms in literature. Some examples are given in order to illustrate the effectiveness of the proposed algorithms. All experiments are carried out on a computer with the aid of programs written in MATLAB.

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6

Čiegis, Raimondas, Remigijus Čiegis, Alexander Jakušev, and Gailė Šaltenienė. "PARALLEL VARIATIONAL ITERATIVE LINEAR SOLVERS." Mathematical Modelling and Analysis 12, no. 1 (March 31, 2007): 1–16. http://dx.doi.org/10.3846/1392-6292.2007.12.1-16.

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In this work we consider parallel variational algorithms for solution of linear systems. Theoretical analysis explains the superlinear convergence rate for two step gradient descent method. A new modification of the algorithm is proposed. Results of computational experiments are given for a linear system of equations approximating 3D elliptic boundary value problem. All algorithms are implemented using parallel array object tool ParSol, then a parallel algorithm follows semi‐automatically from the serial one. Results of the scalability analysis are presented and the efficiency of the presented parallel algorithm is investigated experimentally.

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7

Silva, Jair, Carla T. L. S. Ghidini, Aurelio R. L. Oliveira, and Marta I. V. Fontova. "A Comparison Among Simple Algorithms for Linear Programming." TEMA (São Carlos) 19, no. 2 (September 12, 2018): 305. http://dx.doi.org/10.5540/tema.2018.019.02.305.

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This paper presents a comparison between a family of simple algorithms for linear programming and the optimal pair adjustment algorithm. The optimal pair adjustment algorithm improvements the convergence of von Neumann's algorithm which is very attractive because of its simplicity. However, it is not practical to solve linear programming problems to optimality, since its convergence is slow. The family of simple algorithms results from the generalization of the optimal pair adjustment algorithm, including a parameter on the number of chosen columns instead of just a pair of them. Such generalization preserves the simple algorithms nice features. Significant improvements over the optimal pair adjustment algorithm were demonstrated through numerical experiments on a set of linear programming problems.

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8

Packel, Edward W. "Do Linear Problems Have Linear Optimal Algorithms?" SIAM Review 30, no. 3 (September 1988): 388–403. http://dx.doi.org/10.1137/1030091.

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9

Creutzig, Jakob, and P. Wojtaszczyk. "Linear vs. nonlinear algorithms for linear problems." Journal of Complexity 20, no. 6 (December 2004): 807–20. http://dx.doi.org/10.1016/j.jco.2004.05.003.

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10

Ploskas, Nikolaos, Nikolaos Samaras, and Jason Papathanasiou. "A Decision Support System for Solving Linear Programming Problems." International Journal of Decision Support System Technology 6, no. 2 (April 2014): 46–62. http://dx.doi.org/10.4018/ijdsst.2014040103.

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Linear programming algorithms have been widely used in Decision Support Systems. These systems have incorporated linear programming algorithms for the solution of the given problems. Yet, the special structure of each linear problem may take advantage of different linear programming algorithms or different techniques used in these algorithms. This paper proposes a web-based DSS that assists decision makers in the solution of linear programming problems with a variety of linear programming algorithms and techniques. Two linear programming algorithms have been included in the DSS: (i) revised simplex algorithm and (ii) exterior primal simplex algorithm. Furthermore, ten scaling techniques, five basis update methods and eight pivoting rules have been incorporated in the DSS. All linear programming algorithms and methods have been implemented using MATLAB and converted to Java classes using MATLAB Builder JA, while the web interface of the DSS has been designed using Java Server Pages.

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11

Amaireh, Anas A., Asem S. Al-Zoubi, and Nihad I. Dib. "The optimal synthesis of scanned linear antenna arrays." International Journal of Electrical and Computer Engineering (IJECE) 10, no. 2 (April 1, 2020): 1477. http://dx.doi.org/10.11591/ijece.v10i2.pp1477-1484.

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In this paper, symmetric scanned linear antenna arrays are synthesized, in order to minimize the side lobe level of the radiation pattern. The feeding current amplitudes are considered as the optimization parameters. Newly proposed optimization algorithms are presented to achieve our target; Antlion Optimization (ALO) and a new hybrid algorithm. Three different examples are illustrated in this paper; 20, 26 and 30 elements scanned linear antenna array. The obtained results prove the effectiveness and the ability of the proposed algorithms to outperform and compete other algorithms like Symbiotic Organisms Search (SOS) and Firefly Algorithm (FA).

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12

Theis, Fabian J., Andreas Jung, Carlos G. Puntonet, and Elmar W. Lang. "Linear Geometric ICA: Fundamentals and Algorithms." Neural Computation 15, no. 2 (February 1, 2003): 419–39. http://dx.doi.org/10.1162/089976603762552979.

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Geometric algorithms for linear independent component analysis (ICA) have recently received some attention due to their pictorial description and their relative ease of implementation. The geometric approach to ICA was proposed first by Puntonet and Prieto (1995). We will reconsider geometric ICA in a theoretic framework showing that fixed points of geometric ICA fulfill a geometric convergence condition (GCC), which the mixed images of the unit vectors satisfy too. This leads to a conjecture claiming that in the nongaussian unimodal symmetric case, there is only one stable fixed point, implying the uniqueness of geometric ICA after convergence. Guided by the principles of ordinary geometric ICA, we then present a new approach to linear geometric ICA based on histograms observing a considerable improvement in separation quality of different distributions and a sizable reduction in computational cost, by a factor of 100, compared to the ordinary geometric approach. Furthermore, we explore the accuracy of the algorithm depending on the number of samples and the choice of the mixing matrix, and compare geometric algorithms with classical ICA algorithms, namely, Extended Infomax and FastICA. Finally, we discuss the problem of high-dimensional data sets within the realm of geometrical ICA algorithms.

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13

Aben, H., and A. Errapart. "Photoelastic Tomography with Linear and Non-linear Algorithms." Experimental Mechanics 52, no. 8 (December 14, 2011): 1179–93. http://dx.doi.org/10.1007/s11340-011-9575-z.

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14

Júdice, Joaquim J. "Algorithms for linear programming with linear complementarity constraints." TOP 20, no. 1 (September 30, 2011): 4–25. http://dx.doi.org/10.1007/s11750-011-0228-2.

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15

Werschulz, Arthur G., and Henryk Woźniakowski. "Are linear algorithms always good for linear problems?" Aequationes Mathematicae 31, no. 1 (December 1986): 202–12. http://dx.doi.org/10.1007/bf02188189.

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16

Abdallah, S., and V. Lesser. "A Multiagent Reinforcement Learning Algorithm with Non-linear Dynamics." Journal of Artificial Intelligence Research 33 (December 17, 2008): 521–49. http://dx.doi.org/10.1613/jair.2628.

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Several multiagent reinforcement learning (MARL) algorithms have been proposed to optimize agents' decisions. Due to the complexity of the problem, the majority of the previously developed MARL algorithms assumed agents either had some knowledge of the underlying game (such as Nash equilibria) and/or observed other agents actions and the rewards they received. We introduce a new MARL algorithm called the Weighted Policy Learner (WPL), which allows agents to reach a Nash Equilibrium (NE) in benchmark 2-player-2-action games with minimum knowledge. Using WPL, the only feedback an agent needs is its own local reward (the agent does not observe other agents actions or rewards). Furthermore, WPL does not assume that agents know the underlying game or the corresponding Nash Equilibrium a priori. We experimentally show that our algorithm converges in benchmark two-player-two-action games. We also show that our algorithm converges in the challenging Shapley's game where previous MARL algorithms failed to converge without knowing the underlying game or the NE. Furthermore, we show that WPL outperforms the state-of-the-art algorithms in a more realistic setting of 100 agents interacting and learning concurrently. An important aspect of understanding the behavior of a MARL algorithm is analyzing the dynamics of the algorithm: how the policies of multiple learning agents evolve over time as agents interact with one another. Such an analysis not only verifies whether agents using a given MARL algorithm will eventually converge, but also reveals the behavior of the MARL algorithm prior to convergence. We analyze our algorithm in two-player-two-action games and show that symbolically proving WPL's convergence is difficult, because of the non-linear nature of WPL's dynamics, unlike previous MARL algorithms that had either linear or piece-wise-linear dynamics. Instead, we numerically solve WPL's dynamics differential equations and compare the solution to the dynamics of previous MARL algorithms.

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17

Perkins, Gavin D., Anthony J. Handley, Violetta Raffay, Koenraad G. Monsieurs, and Maaret Castren. "Resuscitation algorithms—Linear or circular?" Resuscitation 88 (March 2015): e17-e18. http://dx.doi.org/10.1016/j.resuscitation.2015.01.004.

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18

Schmitt, Lothar M., Chrystopher L. Nehaniv, and Robert H. Fujii. "Linear analysis of genetic algorithms." Theoretical Computer Science 200, no. 1-2 (June 1998): 101–34. http://dx.doi.org/10.1016/s0304-3975(98)00004-8.

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19

Sallas, William M., and Helmuth Spath. "Mathematical Algorithms for Linear Regression." Journal of the American Statistical Association 88, no. 421 (March 1993): 376. http://dx.doi.org/10.2307/2290737.

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20

Iglesias, Pablo A. "Algorithms for linear quadratic optimization." Automatica 37, no. 2 (February 2001): 321–22. http://dx.doi.org/10.1016/s0005-1098(00)00149-7.

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21

Brass, Helmut. "Linear Algorithms with Finite Deviation." Journal of Complexity 14, no. 1 (March 1998): 85–101. http://dx.doi.org/10.1006/jcom.1997.0468.

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22

Fabregat-Traver, Diego, and Paolo Bientinesi. "Application-tailored linear algebra algorithms." International Journal of High Performance Computing Applications 27, no. 4 (July 18, 2013): 426–39. http://dx.doi.org/10.1177/1094342013494428.

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23

Betke, U., and P. Gritzmann. "Projection algorithms for linear programming." European Journal of Operational Research 60, no. 3 (August 1992): 287–95. http://dx.doi.org/10.1016/0377-2217(92)90080-s.

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24

Wu, Shiquan, and Fang Wu. "New algorithms for linear programming." Acta Mathematicae Applicatae Sinica 8, no. 1 (January 1992): 18–26. http://dx.doi.org/10.1007/bf02006070.

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25

Dao, Minh N., and Hung M. Phan. "Linear Convergence of Projection Algorithms." Mathematics of Operations Research 44, no. 2 (May 2019): 715–38. http://dx.doi.org/10.1287/moor.2018.0942.

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26

Franek, Frantisek, and Michael Liut. "Computing Maximal Lyndon Substrings of a String." Algorithms 13, no. 11 (November 12, 2020): 294. http://dx.doi.org/10.3390/a13110294.

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There are two reasons to have an efficient algorithm for identifying all right-maximal Lyndon substrings of a string: firstly, Bannai et al. introduced in 2015 a linear algorithm to compute all runs of a string that relies on knowing all right-maximal Lyndon substrings of the input string, and secondly, Franek et al. showed in 2017 a linear equivalence of sorting suffixes and sorting right-maximal Lyndon substrings of a string, inspired by a novel suffix sorting algorithm of Baier. In 2016, Franek et al. presented a brief overview of algorithms for computing the Lyndon array that encodes the knowledge of right-maximal Lyndon substrings of the input string. Among those presented were two well-known algorithms for computing the Lyndon array: a quadratic in-place algorithm based on the iterated Duval algorithm for Lyndon factorization and a linear algorithmic scheme based on linear suffix sorting, computing the inverse suffix array, and applying to it the next smaller value algorithm. Duval’s algorithm works for strings over any ordered alphabet, while for linear suffix sorting, a constant or an integer alphabet is required. The authors at that time were not aware of Baier’s algorithm. In 2017, our research group proposed a novel algorithm for the Lyndon array. Though the proposed algorithm is linear in the average case and has O(nlog(n)) worst-case complexity, it is interesting as it emulates the fast Fourier algorithm’s recursive approach and introduces τ-reduction, which might be of independent interest. In 2018, we presented a linear algorithm to compute the Lyndon array of a string inspired by Phase I of Baier’s algorithm for suffix sorting. This paper presents the theoretical analysis of these two algorithms and provides empirical comparisons of both of their C++ implementations with respect to the iterated Duval algorithm.

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27

Lee Peizong and Z. M. Kedem. "Synthesizing linear array algorithms from nested FOR loop algorithms." IEEE Transactions on Computers 37, no. 12 (1988): 1578–98. http://dx.doi.org/10.1109/12.9735.

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28

SKULRATTANAKULCHAI, SAN, and HAROLD N. GABOW. "COLORING ALGORITHMS ON SUBCUBIC GRAPHS." International Journal of Foundations of Computer Science 15, no. 01 (February 2004): 21–40. http://dx.doi.org/10.1142/s0129054104002285.

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We present efficient algorithms for three coloring problems on subcubic graphs. (A subcubic graph has maximum degree at most three.) The first algorithm is for 4-edge coloring, or more generally, 4-list-edge coloring. Our algorithm runs in linear time, and appears to be simpler than previous ones. The second algorithm is the first randomized EREW PRAM algorithm for the same problem. It uses O(n/ log n) processors and runs in O( log n) time with high probability, where n is the number of vertices of the graph. The third algorithm is the first linear-time algorithm to 5-total-color subcubic graphs. The fourth algorithm generalizes this to get the first linear-time algorithm to 5-list-total-color subcubic graphs. Our sequential algorithms are based on a method of ordering the vertices and edges by traversing a spanning tree of a graph in a bottom-up fashion. Our parallel algorithm is based on a simple decomposition principle for subcubic graphs.

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29

Da̧browska, Dorota. "Linear algorithms for recovering linear functionals from jittered information." Journal of Complexity 19, no. 4 (August 2003): 555–63. http://dx.doi.org/10.1016/s0885-064x(03)00046-3.

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30

Packel, Edward W. "Linear problems (with extended range) have linear optimal algorithms." Aequationes Mathematicae 31, no. 1 (December 1986): 18–25. http://dx.doi.org/10.1007/bf02188168.

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31

Sabharwal, Chaman Lal. "An Iterative Hybrid Algorithm for Roots of Non-Linear Equations." Eng 2, no. 1 (March 8, 2021): 80–98. http://dx.doi.org/10.3390/eng2010007.

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Finding the roots of non-linear and transcendental equations is an important problem in engineering sciences. In general, such problems do not have an analytic solution; the researchers resort to numerical techniques for exploring. We design and implement a three-way hybrid algorithm that is a blend of the Newton–Raphson algorithm and a two-way blended algorithm (blend of two methods, Bisection and False Position). The hybrid algorithm is a new single pass iterative approach. The method takes advantage of the best in three algorithms in each iteration to estimate an approximate value closer to the root. We show that the new algorithm outperforms the Bisection, Regula Falsi, Newton–Raphson, quadrature based, undetermined coefficients based, and decomposition-based algorithms. The new hybrid root finding algorithm is guaranteed to converge. The experimental results and empirical evidence show that the complexity of the hybrid algorithm is far less than that of other algorithms. Several functions cited in the literature are used as benchmarks to compare and confirm the simplicity, efficiency, and performance of the proposed method.

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32

Zhang, Ruimeng, Yan Zhang, Jinping Sun, and Qing Li. "Pattern Synthesis of Linear Antenna Array Using Improved Differential Evolution Algorithm with SPS Framework." Sensors 20, no. 18 (September 10, 2020): 5158. http://dx.doi.org/10.3390/s20185158.

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In this paper, an improved differential evolution (DE) algorithm with the successful-parent-selecting (SPS) framework, named SPS-JADE, is applied to the pattern synthesis of linear antenna arrays. Here, the pattern synthesis of the linear antenna arrays is viewed as an optimization problem with excitation amplitudes being the optimization variables and attaining sidelobe suppression and null depth being the optimization objectives. For this optimization problem, an improved DE algorithm named JADE is introduced, and the SPS framework is used to solve the stagnation problem of the DE algorithm, which further improves the DE algorithm’s performance. Finally, the combined SPS-JADE algorithm is verified in simulation experiments of the pattern synthesis of an antenna array, and the results are compared with those obtained by other state-of-the-art random optimization algorithms. The results demonstrate that the proposed SPS-JADE algorithm is superior to other algorithms in the pattern synthesis performance with a lower sidelobe level and a more satisfactory null depth under the constraint of beamwidth requirement.

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33

Ravipudi, Jaya Lakshmi. "Synthesis of Linear, Planar, and Concentric Circular Antenna Arrays Using Rao Algorithms." International Journal of Applied Evolutionary Computation 11, no. 3 (July 2020): 31–49. http://dx.doi.org/10.4018/ijaec.2020070103.

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The aim of this paper is to display the efficacy of three newly proposed optimization algorithms named as Rao-1, Rao-2, and Rao-3 in synthesizing antenna arrays. The algorithms are applied to three different antenna array configurations. Thinned arrays with isotropic radiators are considered and the main objective is to find the optimal configuration of ON/OFF elements that produce low side lobe levels. The results of Rao-1, Rao-2, and Rao-3 algorithms are compared with those of improved genetic algorithm (IGA), hybrid Taguchi binary particle swarm optimization (HTBPSO), teaching-learning-based optimization (TLBO), the firefly algorithm (FA), and biogeography-based optimization (BBO). The Rao-1, Rao-2, and Rao-3 algorithms were able to realize antenna arrays having lower side lobe levels (SLL) when compared to the other optimization algorithms.

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34

Alrawashdeh, Mufda Jameel, Taha Radwan Radwan, and Kalid Abunawas Abunawas. "Performance of Linear Discriminant Analysis Using Different Robust Methods." European Journal of Pure and Applied Mathematics 11, no. 1 (January 30, 2018): 284. http://dx.doi.org/10.29020/nybg.ejpam.v11i1.3176.

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This study aims to combine the new deterministic minimum covariance determinant (DetMCD) algorithm with linear discriminant analysis (LDA) and compare it with the fast minimum covariance determinant (FastMCD), fast consistent high breakdown (FCH), and robust FCH (RFCH) algorithms. LDA classifies new observations into one of the unknown groups and it is widely used in multivariate statistical analysis. The LDA mean and covariance matrix parameters are highly influenced by outliers. The DetMCD algorithm is highly robust and resistant to outliers and it is constructed to overcome the outlier problem. Moreover, the DetMCD algorithm is used to estimate location and scatter matrices. The DetMCD, FastMCD, FCH, and RFCH algorithms are applied to estimate misclassification probability using robust LDA. All the algorithms are expected to improve the LDA model for classification purposes in banks, such as bankruptcy and failures, and to distinguish between Islamic and conventional banks. The performances of the estimators are investigated through simulation and actual data.

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35

Han, F., X. Huang, E. Teye, H. Gu, H. Dai, and L. Yao. "A nondestructive method for fish freshness determination with electronic tongue combined with linear and non-linear multivariate algorithms." Czech Journal of Food Sciences 32, No. 6 (November 27, 2014): 532–37. http://dx.doi.org/10.17221/88/2014-cjfs.

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Electronic tongue coupled with linear and non-linear multivariate algorithms was attempted to address the drawbacks of fish freshness detection. Parabramis pekinensis fish samples stored at 4°C were used. Total volatile basic nitrogen (TVB-N) and total viable count (TVC) of the samples were measured. Fisher liner discriminant analysis (Fisher LDA) and support vector machine (SVM) were applied comparatively to classify the samples stored at different days. The results revealed that SVM model was better than Fisher LDA model with a higher identification rate of 97.22% in the prediction set. Partial least square (PLS) and support vector regression (SVR) were applied comparatively to predict the TVB-N and TVC values. The quantitative models were evaluated by the root mean square error of prediction (RMSEP) and the correlation coefficient in the prediction set (R<sub>pre</sub>). The results revealed that SVR model was superior to PLS model with RMSEP = 5.65 mg/100 g, R<sub>pre</sub> = 0.9491 for TVB-N prediction and RMSEP = 0.73 log CFU/g, R<sub>pre</sub> = 0.904 for TVC prediction. This study demonstrated that the electronic tongue together with SVM and SVR has a great potential for a convenient and nondestructive detection of fish freshness.  

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36

Welling, Max, and Yee Whye Teh. "Linear Response Algorithms for Approximate Inference in Graphical Models." Neural Computation 16, no. 1 (January 1, 2004): 197–221. http://dx.doi.org/10.1162/08997660460734056.

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Belief propagation (BP) on cyclic graphs is an efficient algorithm for computing approximate marginal probability distributions over single nodes and neighboring nodes in the graph. However, it does not prescribe a way to compute joint distributions over pairs of distant nodes in the graph. In this article, we propose two new algorithms for approximating these pairwise probabilities, based on the linear response theorem. The first is a propagation algorithm that is shown to converge if BP converges to a stable fixed point. The second algorithm is based on matrix inversion. Applying these ideas to gaussian random fields, we derive a propagation algorithm for computing the inverse of a matrix.

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37

Demmel, James, Ioana Dumitriu, Olga Holtz, and Plamen Koev. "Accurate and efficient expression evaluation and linear algebra." Acta Numerica 17 (April 25, 2008): 87–145. http://dx.doi.org/10.1017/s0962492906350015.

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We survey and unify recent results on the existence of accurate algorithms for evaluating multivariate polynomials, and more generally for accurate numerical linear algebra with structured matrices. By ‘accurate’ we mean that the computed answer has relative error less than 1, i.e., has some correct leading digits. We also address efficiency, by which we mean algorithms that run in polynomial time in the size of the input. Our results will depend strongly on the model of arithmetic: most of our results will use the so-called traditional model (TM), where the computed result of op(a, b), a binary operation like a+b, is given by op(a, b) * (1+δ) where all we know is that |δ| ≤ ε ≪ 1. Here ε is a constant also known as machine epsilon.We will see a common reason for the following disparate problems to permit accurate and efficient algorithms using only the four basic arithmetic operations: finding the eigenvalues of a suitably discretized scalar elliptic PDE, finding eigenvalues of arbitrary products, inverses, or Schur complements of totally non-negative matrices (such as Cauchy and Vandermonde), and evaluating the Motzkin polynomial. Furthermore, in all these cases the high accuracy is ‘deserved’, i.e., the answer is determined much more accurately by the data than the conventional condition number would suggest.In contrast, we will see that evaluating even the simple polynomial x + y + z accurately is impossible in the TM, using only the basic arithmetic operations. We give a set of necessary and sufficient conditions to decide whether a high accuracy algorithm exists in the TM, and describe progress toward a decision procedure that will take any problem and provide either a high-accuracy algorithm or a proof that none exists.When no accurate algorithm exists in the TM, it is natural to extend the set of available accurate operations by a library of additional operations, such as x + y + z, dot products, or indeed any enumerable set which could then be used to build further accurate algorithms. We show how our accurate algorithms and decision procedure for finding them extend to this case.Finally, we address other models of arithmetic, and the relationship between (im)possibility in the TM and (in)efficient algorithms operating on numbers represented as bit strings.

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38

Azouaoui, Ahmed, Mostafa Belkasmi, and Abderrazak Farchane. "Efficient Dual Domain Decoding of Linear Block Codes Using Genetic Algorithms." Journal of Electrical and Computer Engineering 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/503834.

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A computationally efficient algorithm for decoding block codes is developed using a genetic algorithm (GA). The proposed algorithm uses the dual code in contrast to the existing genetic decoders in the literature that use the code itself. Hence, this new approach reduces the complexity of decoding the codes of high rates. We simulated our algorithm in various transmission channels. The performance of this algorithm is investigated and compared with competitor decoding algorithms including Maini and Shakeel ones. The results show that the proposed algorithm gives large gains over the Chase-2 decoding algorithm and reach the performance of the OSD-3 for some quadratic residue (QR) codes. Further, we define a new crossover operator that exploits the domain specific information and compare it with uniform and two point crossover. The complexity of this algorithm is also discussed and compared to other algorithms.

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39

Bidabad, Bijan. "New Algorithms for L1 Norm Regression." Bangladesh Journal of Multidisciplinary Scientific Research 1, no. 1 (June 12, 2019): 1–18. http://dx.doi.org/10.46281/bjmsr.v1i1.311.

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In this paper, we propose four algorithms for L1 norm computation of regression parameters, where two of them are more efficient for simple and multiple regression models. However, we start with restricted simple linear regression and corresponding derivation and computation of the weighted median problem. In this respect, a computing function is coded. With discussion on the m parameters model, we continue to expand the algorithm to include unrestricted simple linear regression, and two crude and efficient algorithms are proposed. The procedures are then generalized to the m parameters model by presenting two new algorithms, where the algorithm 4 is selected as more efficient. Various properties of these algorithms are discussed.

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40

Wang, Pei, Xu Sheng Yang, Zhuo Yuan Wang, Lin Gong Li, Ji Chang He, and Qing Jie Wang. "Solving Large-Scale Asymmetric Sparse Linear Equations Based on SuperLU Algorithm." Advanced Materials Research 230-232 (May 2011): 1355–61. http://dx.doi.org/10.4028/www.scientific.net/amr.230-232.1355.

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This article introduces the recent research of SuperLU algorithms and the optimal storage method for [1] the sparse linear equations of coefficient matrix. How to solve large-scale non-symmetric sparse linear equations by SuperLU algorithm is the key part of this article. The advantage of SuperLU algorithm compared to other algorithms is summarized at last. SuperLU algorithm not only saves memory space, but also reduces the computation time. Because of less storage needed by this algorithm, it could solve equation with larger scale, which is much more useful.

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41

Plaksienko, V. S. "Linear-logical decision-making algorithm for signal processing." Vestnik of Don State Technical University 18, no. 4 (January 9, 2019): 385–91. http://dx.doi.org/10.23947/1992-5980-2018-18-4-385-391.

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Introduction. Heuristic synthesis is used to improve the efficiency of reception and processing of discrete signals under aprior information pressure. The analysis of the decisionmaking algorithm for the linear-logical processing of discrete signals in case of the incomplete aprior data on their parameters is presented. The work objective is to develop and analyze the efficiency of the linear-logical algorithms.Materials and Methods. New mathematical algorithms for the signal reception and processing, effective under conditions of a priori uncertainty, are proposed. They are based on the consideration of the structure of emissions and process exceedance in the signal processing channels.Research Results. Linear-logical algorithms for processing discrete signals are developed. They are based on the consideration of one, two and more detailed characteristics of emissions or exceedance of random processes.Discussion and Conclusion. The results obtained can be useful in the synthesis of algorithms and devices for the signal reception and processing. Algorithms and devices are implemented both in an analog form and in the form of algorithms for computers. The simulation programs for the signal processing under conditions of the considerable uncertainty of aprior information on the signals and the channels of their distribution are developed.

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Chen, Chin Chun, Yuan Horng Lin, Jeng Ming Yih, and Sue Fen Huang. "Construct Knowledge Structure of Linear Algebra." Advanced Materials Research 211-212 (February 2011): 793–97. http://dx.doi.org/10.4028/www.scientific.net/amr.211-212.793.

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Apply interpretive structural modeling to construct knowledge structure of linear algebra. New fuzzy clustering algorithms improved fuzzy c-means algorithm based on Mahalanobis distance has better performance than fuzzy c-means algorithm. Each cluster of data can easily describe features of knowledge structures individually. The results show that there are six clusters and each cluster has its own cognitive characteristics. The methodology can improve knowledge management in classroom more feasible.

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Boffey, T. B., and Dimitri P. Bertsekas. "Linear Network Optimization: Algorithms and Codes." Journal of the Operational Research Society 45, no. 4 (April 1994): 483. http://dx.doi.org/10.2307/2584223.

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Pedraza, Luis, Cesar Hernandez, Ingrid Paez, Jorge Ortiz, and E. Rodriguez-Colina. "Linear Algorithms for Radioelectric Spectrum Forecast." Algorithms 9, no. 4 (December 2, 2016): 82. http://dx.doi.org/10.3390/a9040082.

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Wagner, Donald K., and Dimitri P. Bertsekas. "Linear Network Optimization: Algorithms and Codes." Mathematics of Computation 60, no. 202 (April 1993): 872. http://dx.doi.org/10.2307/2153140.

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Perez-Jimenez, Alberto J., and Juan C. Perez-Cortes. "Genetic algorithms for linear feature extraction." Pattern Recognition Letters 27, no. 13 (October 2006): 1508–14. http://dx.doi.org/10.1016/j.patrec.2006.02.011.

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Hachtel, G. D., and C. R. Morrison. "Linear complexity algorithms for hierarchical routing." IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 8, no. 1 (1989): 64–80. http://dx.doi.org/10.1109/43.21820.

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Sameh, Ahmed H., and Vivek Sarin. "Parallel algorithms for indefinite linear systems." Parallel Computing 28, no. 2 (February 2002): 285–99. http://dx.doi.org/10.1016/s0167-8191(01)00140-5.

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Boffey, T. B. "Linear Network Optimization: Algorithms and Codes." Journal of the Operational Research Society 45, no. 4 (April 1994): 483. http://dx.doi.org/10.1057/jors.1994.70.

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Wright, Stephen J. "Parallel Algorithms for Banded Linear Systems." SIAM Journal on Scientific and Statistical Computing 12, no. 4 (July 1991): 824–42. http://dx.doi.org/10.1137/0912044.

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