Related papers: Some Historical Aspects of Error Calculus by Diric…
Several results are obtained concerning the function $\Delta_k(x)$, which represents the error term in the general Dirichlet divisor problem. These include the estimates for the integral of this function, as well as for the corresponding…
We describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…
Methods are developed for eliciting a Dirichlet prior based upon bounds on the individual probabilities that hold with virtual certainty. This approach to selecting a prior is applied to a contingency table problem where it is demonstrated…
Let $\Delta(x)$ be the error term of the Dirichlet divisor problem. An asymptotic formula with the error term $O(T^{53/28+\epsilon})$ is established for the integral $\int_1^T\Delta^4(x)dx.$ Similar results are also established for some…
Finite precision computations using digital computers involve the following inherent errors: (1) Round-off error of finite precision computations (2) Binary computer arithmetic precludes exact number representation of traditional decimal…
The history of the development of the concept of complex numbers from the 16th to 19th centuries. The origin and refinement of the geometric and physical meaning of complex numbers, the emergence of vectoral analysis.
Error control by means of a posteriori error estimators or indica-tors and adaptive discretizations, such as adaptive mesh refinement, have emerged in the late seventies. Since then, numerous theoretical developments and improvements have…
Interval calculus is a relatively new branch of mathematics. Initially understood as a set of tools to assess the quality of numerical calculations (rigorous control of rounding errors), it became a discipline in its own rights today.…
We study the distribution functions of several classical error terms in analytic number theory, focusing on the remainder term in the Dirichlet divisor problem $\Delta(x)$. We first bound the discrepancy between the distribution function of…
This paper describes types of errors arising in a recently proposed method of incidence estimation from prevalence data. The errors are illustrated by a simulation study about a hypothetical irreversible disease. In addition, a way of…
Large-scale computer experiments are becoming increasingly important in science. A multi-step procedure is introduced to statisticians for modeling such experiments, which builds an accurate interpolator in multiple steps. In practice, the…
The choice of a point set, to be used in numerical integration, determines, to a large extent, the error estimate of the integral. Point sets can be characterized by their discrepancy, which is a measure of its non-uniformity. Point sets…
Dirichlet distributions are probability measures on the unit simplex. They are often used as prior distributions in modeling categorical data, such as in topic analysis of text data. Motivated by this application, we consider Monte Carlo…
Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we…
In this study, we introduce a refined method for ascertaining error estimations in numerical simulations of dynamical systems via an innovative application of composition techniques. Our approach involves a dual application of a basic…
The error on a real quantity Y due to the graduation of the measuring instrument may be represented, when the graduation is regular and fines down, by a Dirichlet form on R whose square field operator do not depend on the probability law of…
We relate the convergence of time-changed processes driven by fractional equations to the convergence of corresponding Dirichlet forms. The fractional equations we dealt with are obtained by considering a general fractional operator in…
We survey the classical results of the Dirichlet Approximation Theorem.
Accuracy-driven computation is a strategy widely used in exact-decisions number types for robust geometric algorithms. This work provides an overview on the usage of error bounds in accuracy-driven computation, compares different approaches…
The paper deals with finite element approximations of elliptic Dirichlet boundary control problems posed on two-dimensional polygonal domains. Error estimates are derived for the approximation of the control and the state variables. Special…