Interval mathematics algorithms for tolerance analysis

Two iterative algorithms for tolerance analysis of linear electrical circuits are suggested. They are based on the mean-value-form representation of the function considered and involve the internal computation of its first-order partial derivatives. Two modified mean-value forms for computing the interval extensions of multivariate functions are introduced. It is proved that under appropriate conditions these forms assure narrower interval enclosures of the range as compared with other known forms. Thus the use of the modified mean-value forms substantially improves the convergence speed of algorithms. The improved mechanical efficiency of the algorithms is illustrated by three examples, confirming that they require less computer time and memory volume than other first-order interval techniques