Matrix decomposition, when the rating matrix has missing values, is recognized as an outstanding technique for recommendation system. In order to approximate user-item rating matrix, we construct loss function and append regularization constraint to prevent overfitting. Thus, the solution of matrix decomposition becomes an optimization problem. Alternating least squares (ALS) and stochastic gra...

in this paper, we propose and analyze an efficient matrix methodbased on bell polynomials for numerically solving nonlinear fredholm- volterraintegral equations. for this aim, first we calculate operational matrix of integration and product based on bell polynomials. by using these matrices, nonlinearfredholm-volterra integral equations reduce to the system of nonlinear algebraicequations which...

lsmr (least squares minimal residual) is an iterative method for the solution of the linear system of equations and leastsquares problems. this paper presents a block version of the lsmr algorithm for solving linear systems with multiple right-hand sides. the new algorithm is based on the block bidiagonalization and derived by minimizing the frobenius norm of the resid ual matrix of normal equa...

In this paper, an iterative method is proposed for solving large general Sylvester matrix equation $AXB+CXD = E$, where $A in R^{ntimes n}$ , $C in R^{ntimes n}$ , $B in R^{stimes s}$ and  $D in R^{stimes s}$ are given matrices and $X in R^{stimes s}$  is the unknown matrix. We present a global conjugate gradient (GL-CG) algo- rithm for solving linear system of equations with multiple right-han...

in this paper, an iterative method is proposed for solving large general sylvester matrix equation $axb+cxd = e$, where $a in r^{ntimes n}$ , $c in r^{ntimes n}$ , $b in r^{stimes s}$ and  $d in r^{stimes s}$ are given matrices and $x in r^{stimes s}$  is the unknown matrix. we present a global conjugate gradient (gl-cg) algo- rithm for solving linear system of equations with multiple right-han...

in the present paper, we introduce the sequence space [{l_p}(e,delta) = left{ x = (x_n)_{n = 1}^infty : sum_{n = 1}^infty left|  sum_{j in {e_n}} x_j - sum_{j in e_{n + 1}} x_jright| ^p < infty right},] where $e=(e_n)$ is a partition of finite subsets of the positive integers and $pge 1$. we investigate its topological properties and inclusion relations. moreover, we consider the problem of fin...

In this paper, the min-time optimal control problem is mainly investigated in the linear time invariant (LTI) continuous-time control system with a constrained input. A high order dynamical LTI system is firstly considered for this purpose. Then the Pontryagin principle and some necessary optimality conditions have been simultaneously used to solve the optimal control problem. These optimality ...

The linear system of equations Ax = b where A = [aij ] in Cn.n is a crispsingular matrix and the right-hand side is a fuzzy vector is called a singularfuzzy linear system of equations. In this paper, solving singular fuzzy linearsystems of equations using generalized inverses such as Drazin inverse andpseudo-inverse are investigated.

This investigation deals with transient analysis of cold standby system with n units . Chapman-Kolmogorov equations are developed for repair facility with two repairmen and solved by using matrix technique. Availability and reliability factors have been obtained with probability of the system. A particular case has also been discussed.