The computation of two Bayesian predictive distributions which are discrete mixtures of incomplete beta functions is considered. The number of iterations can easily become large for these distributions and thus, the accuracy of the result can be questionable. Therefore, existing algorithms for that class of mixtures are improved by introducing round-off error calculation into the stopping rule....

In updating algorthms where orthogonal transformations are accumulated , it is important to preserve the orthogonality of the product in the presence of rounding error. Moonen, Van Dooren, and Vandewalle have pointed out that simply normalizing the columns of the product tends to preserve orthogonality | though not, as DeGroat points out, to working precision. In this note we give an analysis o...

Abstract In this paper, an incremental quaternion interpolation algorithm is introduced. With the assumption of a constant interval between a pair of quaternions, the cost of interpolation algorithm is significantly reduced. Expensive trigonometric calculations in Slerp are replaced with simple linear combination arithmetic. The round-off errors and drifting behavior accumulated through increme...

This paper draws attention to the risk of rounding error in the numerical evaluation of steady-state probabilities for the M/M family of queues. A method for avoiding the risk is presented which is easy to program for calculation in practice.

In several recent publications, numerical integrators based on Jacobi elliptic functions are proposed for solving the equations of motion of the rigid body. Although this approach yields theoretically the exact solution, a standard implementation shows an unexpected linear propagation of round-off errors. We explain how deterministic error contribution can be avoided, so that round-off behaves ...

This paper draws attention to the risk of rounding error in the numerical evaluation of steady-state probabilities for the M/M family of queues. A method for avoiding the risk is presented which is easy to program for calculation in practice.

We determine for which rouiidings adrlitioii in the floating-point screen has representable rounding error, whicli rouiiclings are implied by truncation of digit strings i n different radix systems with contiguous digits, and how rnany additional digits (including possibly a sticky bit) have to I)c kept in such systems in orcler to perforin a given rorinclirig correctly. Throughout the paper, w...

Financial prices are often discretized to the nearest cent, for example. Thus we can say that prices are observed with rounding error. Rounding errors affect the estimation of volatility. Understanding them becomes important especially when we use high frequency data. In this setting, we study the asymptotic behavior of the Realized Volatility (RV), which is commonly used as an estimator of the...

The aim of this paper is to find an accurate and efficient algorithm for evaluating the summation of large sets of floating-point numbers. We present a new representation of the floating-point number system in which a number is represented as a linear combination of integers and the coefficients are powers of the base of the floating-point system. The approach allows to build up an accurate flo...