Interval Arithmetic. In this section, we briefly explain

interval arithmetic and notion.

Some Properties of the

Interval Arithmetic Operations.

In [14], particle swarm optimization (PSO) technique is combined with

interval arithmetic to realize array synthesis in the presence of array excitation amplitude error.

Furthermore it is caused by the intrinsic wrapping effect of the

interval arithmetic. Although the overestimation is obvious, the overestimation is controlled in reasonable range.

The values of [[epsilon].sub.L.sub.i] and [[epsilon].sub.U.sub.i] can be determined using

interval arithmetic (defined in Section 2).

The canonical self-validated computation model is

interval arithmetic. Several other models have been designed to produce more accurate error estimates, usually by storing more information about the computed quantities and how they relate to the input data.

The enclosure property (1.4) carries over to expressions: If r([x.sub.1],...,[x.sub.n]) is an arithmetic expression in the variables [x.sub.1],..., [x.sub.n], then its

interval arithmetic evaluation r([x.sub.1],..., [x.sub.n]), an interval, contains the range of r for

Interval extensions are functions where

interval arithmetic is applied to calculate results.

Yang (2004) Fuzzy AHP based on the (A) Confidence interval fuzzy

interval arithmetic and geometric mean and confidence levels with approach express the interval mean approach.

Papers from a June 2009 symposium are presented here, in sections on algorithms and number systems, arithmetic hardware, finite fields and cryptography, mathematical software, decimal hardware, floating-point techniques, decimal transcendents, automated synthesis of arithmetic operations, decimal arithmetic in industry, and

interval arithmetic. Specific topics covered include polynomial multiplication over finite fields using field extensions and interpolation, fast and accurate Bessel function computation, certified and fast computation of supremum norms of approximation errors, and computation of decimal transcendental functions using the CORDIC algorithm.

Unfortunately, most hardware and software systems do not support an

interval arithmetic data type.

The possibility of estimating bounds for this econometric likelihood function by balanced random

interval arithmetic is experimentally investigated in (Zilinskas and Bogle 2006).