ORIGINAL_ARTICLE $2n$-by-$2n$ circulant preconditioner for a kind of spatial fractional diffusion equations In this paper, a $2n$-by-$2n$ circulant preconditioner  is introduced for a system of linear equations arising from discretization of the spatial fractional diffusion equations (FDEs). We show that the eigenvalues of our preconditioned system  are clustered around 1, even if the diffusion coefficients of FDEs are not constants. Numerical experiments are presented to demonstrate that the preconditioning technique is very efficient. https://jmm.guilan.ac.ir/article_4013_fe2cb10372a1363c89f327e7cdd86bc4.pdf 2020-06-01 207 218 10.22124/jmm.2020.15908.1391 Fractional diffusion equation circulant matrix skew-circulant matrix Toeplitz matrix Krylov subspace methods Naser Akhoundi akhoundi@du.ac.ir 1 School of mathematics and computer science, Damghan university, Damghan, Iran LEAD_AUTHOR
ORIGINAL_ARTICLE A simulated annealing algorithm for the restricted stochastic traveling salesman problem with exponentially distributed arc lengths The considered stochastic travelling salesman problem is defined where the costs are distributed exponentially. The costs are symmetric and they satisfy the triangular inequality. A discrete time Markov chain is established in some periods of time. A stochastic tour is created in a dynamic recursive way and the best node is detected to traverse in each period. Then, a simulated annealing based heuristic method is applied to select the best state. All the nodes should be traversed exactly once. An initial $\rho$-approximate solution is applied for some benchmark problems and the obtained solutions are improved by a simulated annealing heuristic method. https://jmm.guilan.ac.ir/article_4027_7430873ed63a7620715be6db6623dc1b.pdf 2020-06-01 279 290 10.22124/jmm.2020.15535.1378 Travelling salesman problem discrete time Markov chain approximation algorithms Simulated Annealing Mohsen Abdolhosseinzadeh mohsen.ab@ubonab.ac.ir 1 Department of Mathematics, University of Bonab, Bonab, Iran LEAD_AUTHOR Mir Mohammad Alipour alipour@ubonab.ac.ir 2 Department of Computer Engineering, University of Bonab, Bonab, Iran AUTHOR
ORIGINAL_ARTICLE A survey on compressive sensing: classical results and recent advancements Recovering sparse signals from linear measurements has demonstrated outstanding utility in a vast variety of real-world applications.  Compressive sensing is the topic that studies the associated raised questions for the possibility of a successful recovery. This topic is well-nourished and numerous results are available in the literature. However, their dispersity makes it  time-consuming for  practitioners to quickly grasp its main ideas and classical algorithms, and further touch upon the recent advancements. In this survey, we overview vital classical  tools and algorithms in compressive sensing and describe its significant recent advancements. We conclude  by a numerical comparison of the performance of described approaches. https://jmm.guilan.ac.ir/article_4155_b84c66cd66053821ec4e8c2447fd3bf1.pdf 2020-06-01 309 344 10.22124/jmm.2020.16701.1450 compressive sensing $ell_p$ recovery greedy algorithms Ahmad Mousavi amousavi@umn.edu 1 Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN, USA LEAD_AUTHOR Mehdi Rezaee rezaee1@umbc.edu 2 Department of Computer Science and Electrical Engineering, University of Maryland Baltimore County, Baltimore, MD 21250, USA AUTHOR Ramin Ayanzadeh ayanzadeh@umbc.edu 3 Department of Computer Science and Electrical Engineering, University of Maryland Baltimore County, Baltimore, MD 21250, USA AUTHOR