Abstract
A real number can be represented as a sequence of nested, closed intervals whose lengthes tend to zero. In the LFT approach to Exact Real Arithmetic the sequence of intervals is generated by a sequence of one-dimensional linear fractional transformations (1-LFTs) applied to a base interval, [9,13,11,4,12,7].
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References
Di Gianantonio, P.: A Golden Ratio Notation for the Real Numbers. CWI Technical Report (1991).
Edalat, A.: Domains for Computation in Mathematics, Physics and Exact Real Arithmetic. Bulletin of Symbolic Logic, Vol. 3 (1997).
Edalat, A., Heckmann R.: Computation with Real Numbers. Applied Semantics Summer School, APPSEM 2000 (2000).
Edalat, A., Potts, P. J.: A New Representation for Exact Real Numbers. Electronic Notes in Theoretical Computer Science, Vol. 6 (1997).
Errington, L., Heckmann, R.: Using the C-LFT Library (2000).
Gosper, R. W.: Continued Fraction Arithmetic. HAKMEM Item 101B, MIT AI Memo 239, MIT (1972).
Heckmann, R.: How Many Argument Digits are Needed to Produce n Result Digits? Electronic Notes in Theoretical Computer Science, Vol. 24 (2000).
Kelsey, T. W.: Exact Numerical Computation Via Symbolic Computation. Proceedings of Computability and Complexity in Analysis 2000, 187–197 (2000).
Kornerup, P., Matula, D. W.: Finite Precision Lexicographic Continued Fraction Number Systems. Proceedings of 7th IEEE Symposium on Computer Arithmetic, 207–0214 (1985).
Menissier-Morain, V.: Arbitrary Precision Real Arithmetic: Design and Algorithms. Submitted to Journal Symbolic Computation (1996).
Nielsen, A., Kornerup P.: MSBFirst Digit Serial Arithmetic. Journal of Univ. Comp. Science, 1(7):523543 (1995).
Potts, P. J.: Exact Real Arithmetic Using Möbius Transformations. PhD Thesis, University of London, Imperial College (1998).
Vuillemin, J. E.: Exact Real Computer Arithmetic with Continued Fractions. IEEE Transactions on Computers, 39(8):10871105 (1990).
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Krznarić, M. (2001). Computing a Required Absolute Precision from a Stream of Linear Fractional Transformations. In: Blanck, J., Brattka, V., Hertling, P. (eds) Computability and Complexity in Analysis. CCA 2000. Lecture Notes in Computer Science, vol 2064. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45335-0_11
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DOI: https://doi.org/10.1007/3-540-45335-0_11
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