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...

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...

Let us consider the converging sequence generated by successively dividing by two the step size used in an approximation method. With an appropriate stopping criterion, we show that in the last approximation obtained, the significant bits which are not affected by round-off errors are in common with the exact result, up to one. This strategy has been successfully applied to several composite qu...

We give a sharp estimate for the eigenvectors of a positive deenite Hermitian matrix under a oating-point perturbation. The proof is elementary. Recently there have been a number of papers on eigenvector perturbation bounds that involve a perturbation of the matrix which is small in some relative sense, including the typical rounding errors in matrix elements ((1], 2], 10], 8], 4], 5]). The pro...

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...

AbshzctThe statistical analysis of coefficient quantization n o k io digital filters is a useful technique because it gives theoretid and practical results without resorting to lengthy case-by-case trials. The realization problem of digital filters can thus be simplified a n a l f i d y by statistical approaches. Furthermore, statistical approaches have an advantage of supplying unified tools f...

Whilst the development of Learning Classifier Systems has produced excellent results in some fields of application, it has been widely noted that problems emerge when seeking to establish higher levels of knowledge (see Barry (1993) for a relevant review). Tsotsos (1995) suggests that research into the operation of the Visual Cortex shows a hierarchical decomposition of processing more structur...

In the paper: an efficient VLSI architecture for a 8x 8 twodimensional discrete cosine transform and inverse discrete cosine transform (2-D DCTIIDCT) with a new 1-D DCTIIDCT algorithm is presented. The proposed new algorithm makes all coeficients are positive to simplify the design of multipliers and the coefficients have less round-off error than Lee's algorithm [ I ] . For computing 2-D DCTII...

The present investigation designs a systematic method for finding the latent roots and the principal axes of a matrix, without reducing the order of the matrix. It is characterized by a wide field of applicability and great accuracy, since the accumulation of rounding errors is avoided, through the process of "minimized iterations". Moreover, the method leads to a well convergent successive app...