The opportunity for 802.11b WLAN technology is spreading; both in the business and consumer sectors. Journalistic genre in this embryonic area assert that people use WLAN because it liberates them from wires, which enables complete mobility to use WLAN in any location with 802.11b. This study addresses both business and personal sectors, and quantifies where and which specific tasks people enga...

To study the heat or diffusion equation it is often used the Crank-Nicolson method which is unconditionally stable and has order of convergence O(k + h ), where k and h are mesh con2 2 stants. Unfortunately, using this method in conventional floatingpoint arithmetic we get solutions including not only the method error, but also representation and rounding error, Therefore, we propose an interva...

If the complex Schur decomposition is used to solve a real linear system, then the computed solution generally has a complex component because of roundoff error. We show that the real part of the computed solution that is obtained in this way solves a nearby real linear system. Thus, it is “numerically safe” to obtain real solutions to real linear systems via the complex Schur decomposition. Th...

There exists a huge number of numerical methods that iteratively construct approximations to the solution y(x) of an ordinary differential equation (ODE) y(x) = f(x, y) starting from an initial value y0 = y(x0) and using a finite approximation step h that influences the accuracy of the obtained approximation. In this paper, a new framework for solving ODEs is presented for a new kind of a compu...

This correspondence considers error analysis of blockimplemented 2-D digital filters. Expressions for error bound and meansquare error for roundoff error accumulation are derived using fixedpoint arithmetic, and compared with the results obtained usingordinary 2-D difference equations.

The commonly used graded piecewise polynomial collocation method for weakly singular Volterra integral equations may cause serious round-off error problems due to its use of extremely nonuniform partitions and the sensitivity of such time-dependent equations to round-off errors. The singularity preserving (nonpolynomial) collocation method is known to have only local convergence. To overcome th...

Social Media sites provide consumers the ability to publicly create and shape the opinion about products, services and brands. Hence, timely understanding of content created in social media has become a priority for marketing departments, leading to the appearance of social media analysis applications. This article describes an approach to help users of IBM Cognos Consumer Insight, IBM’s social...

Finite difference methods, such as the mid-point rule, have been applied successfully to the numerical solution of ordinary and partial differential equations. If such formulas are applied to observational data, in order to determine derivatives, the results can be disastrous. The reason for this is that measurement errors, and even rounding errors in computer approximations, are strongly ampli...

This paper contains the rounding error analysis for the Chebyshev method for the solution of large linear systems Ax+g = 0 where A = A is positive definite. We prove that the Chebyshev method in floating point arithmetic is numerically stable, which means that the computed sequence {x^} approximates the solution a such that lim|k is of order C||a||.||A~ \\.\\y\\ where £ is the relative computer...

In this paper, we apply the Variation of Parameters Method (VPM) for solving initial and boundary value problems of diversified physical nature. The analytical results are calculated in terms of convergent series with easily computable components. The proposed VPM is applied without any discretization, perturbation, transformation or restrictive assumptions and is free from round off errors and...