Computational Complexity and Feasibility of Data Processing and Interval Computations pp 1-21 | Cite as

# Informal Introduction: Data Processing, Interval Computations, and Computational Complexity

## Abstract

This introduction starts with material aimed mainly at those readers who axe not well familiar with interval computations and/or with the computational complexity aspects of data processing and interval computations. It provides the motivation for the basic mathematical and computational problems that we will be analyzing in this book. Readers who are well familiar with these problems can skip the bulk of this chapter and go straight to the last section that briefly outlines the structure of the book.

_{1},..., x

_{n}) of n real variables, and n intervals x

_{i}, = [x

_{i}, x̄

_{i}], compute the range

A typical application of this problem is: from the measurements, we know the approximate values x̃_{i} of physical quantities x_{i}, and we know the guaranteed accuracy Δ_{i} of each measurement. As a result, we know that x_{i} belongs to the interval x_{i} = [x̃_{i} - Δ_{i}, x̃_{i} + Δ_{i}]. We also know the algorithm f(x_{1},..., x_{n}) that transforms the values x_{i}, into the value of the desired quantity y. We want to know the set of possible values of y. For a continuous function f (x_{1},..., x_{n}), this set is an interval (we will denote it by y = [y, ȳ]). So, the question is: can we compute the endpoints y and y of this interval ȳ in reasonable time?

## Keywords

Arithmetic Operation Interval Computation Guarantee Estimate Exact Range Metic Operation## Preview

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