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 ...

This paper is part of a wide debate and critical reflection on the use of ICT in nursery schools, and focuses on the use of station KidSmart in the classroom to enhance scientific learning within the logical-mathematic field. The study is organized as follows: after presenting the institutional setting within which ICT has been introduced in Italian nursery schools, some considerations are made...

In this paper we present a general library to reason about floating-point numbers within the Coq system. Most of the results of the library are proved for an arbitrary floating-point format and an arbitrary base. A special emphasis has been put on proving properties for exact computing, i.e. computing without rounding errors.

A new treatment for homotopy perturbation method is introduced. The new treatment is called He-Laplacemethodwhich is the coupling of the Laplace transform and the homotopy perturbation method using He’s polynomials. The nonlinear terms can be easily handled by the use of He’s polynomials. The method is implemented on linear and nonlinear partial differential equations. It is found that the prop...

A little known property of a pair of eigenvectors (column and row) of a real tridiagonal matrix is presented. With its help we can define necessary and sufficient conditions for the unique real tridiagonal matrix for which an approximate pair of complex eigenvectors are exact. Similarly we can designate the unique real tridiagonal matrix for which two approximate real eigenvectors, with differe...

Although simple additive weighting method (SAW) is the most popular approach for classical multiple attribute decision making (MADM), it is not practical any more if information is fuzzy. The existing methods of Fuzzy Simple Additive Weighting method (FSAW) apply defuzzification which distorts fuzzy numbers. Furthermore, most of the methods usually require lengthy and laborious manipulations. I...

Certain symmetric linear multistep methods have an excellent long-time behavior when applied to second order Hamiltonian systems with or without constraints. For high accuracy computations round-off can be the dominating source of errors. This article shows how symmetric multistep methods should be implemented, so that round-off errors are minimized and propagate like a random walk.

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...