Jean Vuillemin. Exact real arithmetic with continued fractions. IEEE Transactions on Computers, 39(8):1087--1105, August 1990. Home/Search Document Not in Database Summary Related Articles Check |
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Integration in Real PCF - Edalat, Escardó (1996) (8 citations) (Correct)
....do not produce correct results in practice, due to the presence of roundoff errors. Moreover, they are inappropriate for problems whose solution is sensitive to small variations on the input. As a consequence, exact real number computation has been advocated as an alternative solution (see e.g. [4, 5, 25] on the practical side and e.g. 2, 20, 21, 24, 26, 27, 28] on the foundational side) However, work on exact real number computation has focused on representations of real numbers and has neglected the issue of data types for real numbers. In particular, programming languages for exact real ....
J. Vuillemin. Exact real arithmetic with continued fractions. In Proc. ACM Conferenceon Lisp and Functional Programming, pages 14--27, 1988.
PCF extended with real numbers - Escardo (1996) (7 citations) (Correct)
....giving better and better partial results converging to its value. Keywords: Exact real number computation. Domain Theory and Interval Analysis. Denotational and operational semantics. 1 Introduction There are several practical and theoretical approaches to exact real number computation (see e.g. [7 9,18,21,24,26,30,31,37,39,40,42]) However, the author is not aware of any attempt to give denotational and operational semantics to an implementable programming language with a data type for exact real numbers. Most approaches to exact real number computation are based on representation of real numbers in other data types, such ....
J. Vuillemin. Exact real arithmetic with continued fractions. In Proc. ACM Conference on Lisp and Functional Programming, pages 14--27, 1988.
Integration in Real PCF - Edalat, Escardó (1996) (8 citations) (Correct)
....do not produce correct results in practice, due to the presence of round off errors. Moreover, they are inappropriate for problems whose solution is sensitive to small variations on the input. As a consequence, exact real number computation has been advocated as an alternative solution (see e.g. [7, 8, 42] on the practical side and e.g. 5, 31, 32, 36, 43, 44, 45] on the foundational side) However, work on exact real number computation has focused on representations of real numbers and has neglected the issue of data types for real numbers. In particular, programming languages for exact real ....
J. Vuillemin. Exact real arithmetic with continued fractions. In Proc. ACM Conference on Lisp and Functional Programming, pages 14--27, 1988.
Lazy Functional Algorithms for Exact Real Functionals - Simpson (1998) (11 citations) (Correct)
....for computing quantifiers over streams. Correctness proofs for the algorithms make essential use of domain theory. 1 Introduction In exact real number computation, infinite representations of reals are employed to avoid the usual rounding errors that are inherent in floating point computation [4 6, 17]. For certain real number computations that are highly sensitive to small variations in the input, such rounding errors become inordinately large and the use of floating point algorithms can lead to completely erroneous results [1, 14] In such situations, exact real number computation provides ....
....free to concentrate on the essentials of the algorithms being developed. Also, functional programming naturally supports the recursive definition of functions, which is the most useful method of defining exact functions on real numbers. Such considerations were important motivating factors in [4, 5, 17, 6, 7, 10]. One principal distinguishing feature of functional languages is their acceptance of functions as first class values, and the associated possibility of passing functions as arguments to other function(al)s. In the context of exact real number computation, this raises the question of whether it is ....
J. Vuillemin. Exact real arithmetic with continued fractions. IEEE Transactions on Computers, 39(8):1087--1105, 1990.
Integration in Real PCF - Edalat, Escardó (1996) (8 citations) (Correct)
....not produce correct results in practice, due to the presence of round off errors. Moreover, they are inappropriate for problems whose solution is sensitive to small variations on the input. As a consequence, exact real number computation has been advocated as an alternative solution (see e.g. [4, 5, 20] on the practical side and e.g. 2, 15, 16, 19, 21, 22, 23] on the foundational side) However, work on exact real number computation has focused on representations of real numbers and has neglected the issue of data types for real numbers. In particular, programming languages for exact real ....
J. Vuillemin. Exact real arithmetic with continued fractions. In Proc. ACM Conference on Lisp and Functional Programming, pages 14--27, 1988.
Streaming Representation-Changers - Gibbons (2004) (Correct)
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Jean Vuillemin. Exact real arithmetic with continued fractions. IEEE Transactions on Computers, 39(8):1087--1105, August 1990.
Metamorphisms: Streaming Representation-Changers - Gibbons (2005) (Correct)
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J. Vuillemin, Exact real arithmetic with continued fractions, IEEE Transactions on Computers 39 (8) (1990) 1087--1105.
The constructive reals as a Java Library - Boehm (2004) (Correct)
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J. Vuillemin. Exact real arithmetic with continued fractions. IEEE Transactions on Computers, 39(8):1087--1105, 1990. 12
Streaming Representation-Changers - Gibbons (2004) (Correct)
No context found.
Jean Vuillemin. Exact real arithmetic with continued fractions. IEEE Transactions on Computers, 39(8):1087--1105, August 1990.
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