论文信息 - On interval enclosures using slope arithmetic

On interval enclosures using slope arithmetic

This paper describes how a combination of interval derivative arithmetic and interval slope arithmetic can be used with the programming language Pascal-SC to obtain an enclosure of the range of a factorable function @?:R^n -> R^1 with @? @? C^2 (D) which is often narrower than that which is obtained by using slope arithmetic alone and which is always narrower than that which is obtained by using interval derivative arithmetic alone.

Shen Zuhe | M. A. Wolfe | Shen Zuhe

[1] L. Dixon,et al. Truncated Newton method for sparse unconstrained optimization using automatic differentiation , 1989 .

[2] L. B. Rall,et al. An Introduction to the Scientific Computing Language Pascal-SC (Pascal for Scientific Computation). , 1984 .

[3] L. B. Rall. The Arithmetic of Differentiation , 1986 .

[4] G. Alefeld,et al. Introduction to Interval Computation , 1983 .

[5] Louis B. Rall,et al. Pascal-SC: A computer language for scientific computation , 1987 .

[6] Michael A. Wolfe,et al. ALGLIB, a simple symbol-manipulation package , 1985, CACM.

[7] E. Hansen. Global optimization using interval analysis — the multi-dimensional case , 1980 .

[8] Jon G. Rokne,et al. Computer Methods for the Range of Functions , 1984 .

[9] Anthony S. Wexler. Automatic evaluation of derivatives , 1987 .

[10] Anthony Ralston,et al. Encyclopedia of Computer Science , 1971 .

[11] A. Neumaier,et al. Interval Slopes for Rational Functions and Associated Centered Forms , 1985 .

[12] H Kagiwada,et al. Numerical Derivatives and Nonlinear Analysis , 1986 .

[13] Jon G. Rokne,et al. New computer methods for global optimization , 1988 .

[14] E. Hansen. Global optimization using interval analysis: The one-dimensional case , 1979 .