Application of interval analysis techniques to linear systems. II. The interval matrix exponential function

For pt.I see ibid., vol.35, no.9, p.1129-38 (1988). In part I the authors established new results for continuous and rational interval functions which are of interest in their own right. The authors use these results to study interval matrix exponential functions and to devise a method of constructing augmented partial sums which approximate interval matrix exponential functions as closely as desired. The authors introduce and study 'scalar' and matrix interval exponential functions. These functions are represented as infinite power series and their properties are studied in terms of rational functions obtained from truncations. To determine optimal estimates of error bounds for the truncated series representation of the exponential matrix function, the authors establish appropriate results dealing with Householder norms. In order to reduce the conservativeness for interval arithmetic operations, they consider the nested form for interval polynomials and the centered form for interval arithmetic representations. They also discuss briefly machine bounding arithmetic in digital computers. Finally, the authors present an algorithm for the computation of the interval matrix exponential function which yields prespecified error bounds.<>