| EPSRC Reference: |
GR/L77171/01 |
| Title: |
APPLICATIONS OF EXACT REAL NUMBER COMPUTATION |
| Principal Investigator: |
Edalat, Professor A |
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| Department: |
Computing |
| Organisation: |
Imperial College London |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
21 July 1997 |
Ends: |
20 July 1998 |
Value (£): |
3,400
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| EPSRC Research Topic Classifications: |
| Fundamentals of Computing |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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In our new framework for exact real arithmetic, an extended real number is represented by a shrinking sequence of nested national intervals, encoded by an infinite composition of lfts. The first lft locates the position of the real number under computation in an interval. The remaining lft's have non-negative integer coefficients and give successive refinement of the first interval up to any desired accuracy. All elementary functions are expressed, using the theory of continued fractions and Pad+ approximants, in terms of composition of lft's with two arguments. Apart from elementary functions, we need to be able compute various other functions and operations. We propose to use and adopt various classical results and techniques of interval arithmetic in order to work out new algorithms and techniques for:(i) Efficient handling of comparison, maximum/minimum, absolute value, and definition by cases, (ii) Calculation of the limit of a given convergent sequence of real numbers. The problem is to merge an infinite sequence of infinite streams describing real numbers to one infinite stream describing their limit.(iii) Using the results of the above to compute the value of an infinite sum, the integral of a function as the limit of the sequence of lower or upper Darboux sums, and the Taylor series as a function.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.imperial.ac.uk |