in descriptive statistics, there are two computational algorithms for determining the variance s2, of a set of observations : algorithm 1: s2= - , algorithm 2: s2= , where . it is interesting to discuss, which of the above formulas is numerically more trustworthy in machine numbers sets. i this paper, based on total effect of rounding error, we prove that the second algorithm is better than ...

A bi-objective mathematical model is developed to simultaneously consider the quay crane and yard truck scheduling problems at container terminals. Main real-world assumptions, such as quay cranes with non-crossing constraints, quay cranes’ safety margins and precedence constraints are considered in this model. This integrated approach leads to better efficiency and productivity at container te...

In this paper, a stochastic cell formation problem is studied using queuing theory framework and considering reliability. Since cell formation problem is NP-Hard, two algorithms based on genetic and modified particle swarm optimization (MPSO) algorithms are developed to solve the problem. For generating initial solutions in these algorithms, a new heuristic method is developed, which always cre...

  We present a new full Nesterov and Todd step infeasible interior-point algorithm for semi-definite optimization. The algorithm decreases the duality gap and the feasibility residuals at the same rate. In the algorithm, we construct strictly feasible iterates for a sequence of perturbations of the given problem and its dual problem. Every main iteration of the algorithm consists of a feasibili...

We analyze the behavior of two line arrangement algorithms, a sweepline algorithm and an incremental algorithm, in approximate arithmetic. The algorithms have running times O(n 2 log n) and O(n 2) respectively. We show that each of these algorithms can be implemented to have O(nn) relative error. This means that each algorithm produces an arrangement realized by a set of pseudolines so that eac...

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The desirable features of algorithms for the direct, implicit large-eddy, and largeeddy numerical simulation of compressible turbulent mixing are discussed. Issues specific to turbulence and mixing induced by interfacial instabilities are briefly reviewed. A high-resolution, Eulerian numerical algorithm for compressible turbulent mixing simulations currently in use at the Lawrence Livermore Nat...

We discuss optimality of approximation algorithms and lower bounds on their complexity using Carl’s inequality, which states that for any two Banach spaces X and Y and any α > 0 there exists a constant γα > 0 such that sup 1≤k≤n kek(T ) ≤ γα sup 1≤k≤n kck(T ) holds for all linear and bounded operators T : X → Y . Here ek(T ) is the k-th entropy number of T and ck(T ) is the k-th Gelfand number ...

In this paper, we are interested in some convergent formulations for the unsymmetric collocation method or the so-called Kansa’s method. We review some newly developed theories on solvability and convergence. The rates of convergence of these variations of Kansa’s method are examined and verified in arbitrary–precision computations. Numerical examples confirm with the theories that the modified...

In this expository lecture, we explain how problems of classical polynomial algebra may be understood and numerically solved when they appear in the context of Scientific Computing, i.e. with data of limited accuracy. A suitable conceptual framework is introduced and its use explained in a number of situations.