Experience with a high level language that supports interval arithmetic

An extension of the language S-algol<sup>4</sup> called Triplex<sup>5</sup> which facilitates the use of interval arithmetic and which is similar to triplex algol 60<sup>3</sup> is described. Experience in the use of Triplex is reported. In particular, a Triplex program corresponding to a triplex algol 60 program of Nickel<sup>19</sup> is given, together with numerical results.

[1]  L. B. Rall.  A Comparison of the Existence Theorems of Kantorovich and Moore , 1980 .

[2]  Ronald Morrison,et al.  Triplex: A system for interval arithmetic , 1982, Softw. Pract. Exp..

[3]  Karl Nickel,et al.  The algorithmic language triplex-Algol 60 , 1968 .

[4]  P. J. Landin,et al.  The next 700 programming languages , 1966, CACM.

[5]  Ronald Morrison,et al.  An Introduction to Programming with S-algol , 1982 .

[6]  Götz Alefeld,et al.  Nullstelleneinschließung mit dem Newton-Verfahren ohne Invertierung von Intervallmatrizen , 1972 .

[7]  Eldon Hansen,et al.  Topics in Interval Analysis , 1969 .

[8]  J. M. Yohe.  The Interval Arithmetic Package. , 1977 .

[9]  Eldon Hansen,et al.  A globally convergent interval method for computing and bounding real roots , 1978 .

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

[11]  John F. Wakerly,et al.  The programming language PASCAL , 1979, Microprocessors and microsystems.

[12]  Donald I. Good,et al.  Computer Interval Arithmetic: Definition and Proof of Correct Implementation , 1970, JACM.

[13]  Kaj Madsen,et al.  On the solution of nonlinear equations in interval arithmetic , 1973 .

[14]  Ronald Morrison,et al.  On the Implementation of Constants , 1979, Inf. Process. Lett..

[15]  Gabriele Guenther,et al.  A PROGRAMMING SYSTEM FOR INTERVAL ARITHMETIC IN ALGOL 68 , 1980 .

[16]  Ramon E. Moore.  Methods and applications of interval analysis , 1979, SIAM studies in applied mathematics.