Results Of Arithmetic Operations Research Articles

Some Advantages of the RDM-arithmetic of Intervally-Precisiated Values

AbstractMoore's interval arithmetic always provides the same results of arithmetic operations, e.g. [1, 3]+ [5, 9]= [6, 12]. But in real life problems, the operation result can be different, e.g. equal to [4, 7]. Therefore, real problems require more advanced arithmetic. The paper presents (on example of the division) an arithmetic of intervally-precisiated values (IPV-arithmetic) and its main advantages. Thanks to it, it is possible to process different tasks that people solve intuitively. The most important advantages are: existence of inverse elements of addition and multiplication, holding the distributivity law and the cancellation law of multiplication, possibility of achieving not only the solution span [x, x] but also the full, multidimensional solution and its cardinality distribution without using Monte Carlo method, possibility of achieving unique and complete solution sets of equations with unknowns, possibility of calculations with uncorrelated IPVs, possibility of calculations with fully c...

Bounding the Results of Arithmetic Operations on Random Variables of Unknown Dependency Using Intervals

Many real problems involve calculations on random variables, yet precise details about the correlations or other dependency relationships among those variables are often unknown. For example consider analyzing the cancer risk associated with an environmental contaminant. The dependency of an individual's cumulative exposure on the less useful (but more obtainable) current exposure level will be uncertain. In this and many other cases, data points from which to derive such dependencies are sparse, and obtaining additional data is prohibitively expensive or difficult. Thus manipulating variables whose dependencies are unspecified is a problem of significance. This paper describes a new approach to bounding the results of arithmetic operations on random variables when the dependency relationship between the variables is unspecified. The bounds enclose the space in which the result's distribution function can be.

Accurate measurement of power, energy, and true RMS voltage using synchronous counting

A synchronous measurement method that can be applied for the accurate determination of periodic signals is presented. The method relies on adaptation of the measurement time to the period of the measurement signal. It is based on dual-slope integration performed according to the synchronization signal (input signal). The first phase of integration is fully synchronized with the input signal. The time of the first phase is also measured. The output voltage of the integrator depends directly on the input signal and the time of the first integration phase. Measurement values are the results of arithmetic operations between the time of the second phase of integration and the measuring time (first phase). With this method, an accuracy of 0.1% can be achieved.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Six language extensions to enhance the portability of mathematical software written in PL/I

As part of its revision of ANS PL/I, American National Standards Committee X3J1 is considering extensions like those described here to aid in the development of high-quality portable mathematical software.The new features include environmental enquiry functions, generalization of "restricted expressions" (compile-time expressions), liberalization of the contexts of restricted expressions, a named-literal declaration type, explicit, precision specification for constants, and a pragmatic statement for expressing conditions that an implementation must satisfy for acceptable compilation. Used together, these features will give numerical analysts access to properties of an implementation's floating-point arithmetic in exactly the ways required to ease the burden of tailoring a program's precision specifications to new environments. In many cases it will be possible to write PL/I programs that are completely self-adapting to their host environment.Effective definition of the environmental enquiry functions will require the incorporation of an explicitly parameterized model of floating-point arithmetic; the environmental enquiry functions and the results of arithmetic operations will then be consistently defined in terms of the same parameters. If an appropriate model (to be described in a future paper) is adopted by the Committee and properly integrated into the Standard, a significant advantage will be offered to numerical analysts: they will be able to state and prove theorems about their programs' error bounds by appealing directly to the Standard.In addition to describing the proposed extensions, this paper presents a careful justification and a detailed example of their intended use.None of these features has yet been adopted by X3J1. The Committee is interested in the reactions of the mathematical software community to these ideas and requests that comments be sent to the author.