In this paper, We present the generalizations of the LSMR and NSCG methods for solving matrix equations. First, based on the LSMR algorithm, the Bl-LSMR and Gl-LSMR algorithms are derived by minimizing the Frobenius norm of residual matrix of normal equation. In addition, by extending the idea of LSMR algorithm, we also present the LSMR-M algorithm for solving the general coupled matrix equatio...

Computing solutions of convection-diffusion equations, especially in the convection dominated case, is an important and challenging problem that requires development of fast, reliable numerical methods. We propose a second-order fast explicit operator splitting (FEOS) method based on the Strang splitting. The main idea of the method is to solve the parabolic problem via a discretization of the ...

In this paper, a general system of variational inclusions in Banach Spaces is introduced. An iterative method for finding solutions of a general system of variational inclusions with inverse-strongly accretive mappings and common set of fixed points for a λ-strict pseudocontraction is established. Under certain conditions, by forward-backward splitting method, we prove strong convergence theore...

In this paper, preconditioned iterative methods for solving two-dimensional space-fractional diffusion equations are considered. The fractional diffusion equation is discretized by a second-order finite difference scheme, namely, the Crank-Nicolson weighted and shifted Grünwald difference (CN-WSGD) scheme proposed in [W. Tian, H. Zhou andW. Deng, A class of second order difference approximation...

This work describes a new systematic construction approach for irregular low-density parity-check codes based on the splitting-and-filling technique. The generated code using this proposed method not only has a given degree distribution pair but also has girth of at least six. More importantly, by carefully filling the elements of the variable (check) node sets during the generating process, we...

This paper shows, by means of a new type of operator called a splitting operator, that the Douglas-Rachford splitting method for finding a zero of the sum of two monotone operators is a special case of the proximal point algorithm. Therefore, applications of Douglas-Rachford splitting, such as the alternating direction method of multipliers for convex programming decomposition, are also special...

Almost all known instanton solutions in noncommutative Yang-Mills theory have been obtained in the modified ADHM scheme. In this paper we employ two alternative methods for the construction of the self-dual U(2) BPST instanton on a noncommutative Euclidean four-dimensional space with self-dual noncommutativity tensor. Firstly, we use the method of dressing transformations, an iterative procedur...

In this paper, a new spectral-iterative method is employed to give approximate solutions of fractional logistic differential equation. This approach is based on combination of two different methods, i.e. the iterative method cite{35} and the spectral method. The method reduces the differential equation to systems of linear algebraic equations and then the resulting systems are solved by a numer...