| EPSRC Reference: |
GR/L43077/01 |
| Title: |
EXACT REAL NUMBER COMPUTATION USING LINEAR FRACTIONAL TRANFORMATIONS |
| Principal Investigator: |
Edalat, Professor A |
| Other Investigators: |
|
| Researcher Co-Investigators: |
|
| Project Partners: |
|
| Department: |
Computing |
| Organisation: |
Imperial College London |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
31 March 1998 |
Ends: |
29 September 2001 |
Value (£): |
177,701
|
| EPSRC Research Topic Classifications: |
| Fundamentals of Computing |
|
|
| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
|
|
| Related Grants: |
|
| Panel History: |
|
|
Summary on Grant Application Form |
|
Numerical computation is fundamental in almost all areas of science, technology and finance. At the present time, floating-point representation is the basis of computer arithmetic. However, reliability issues are of major influence in many applications. When the solution of a problem involves a large amount of floating-point computations, round-off errors may well produce grossly inaccurate or even incorrect results. Two frameworks for exact real number computation have been proposed, one based on B-adic numbers and one on continued fractions. We have recently developed a simple representation of real numbers by linear fractional transformations, with a prototype implementation in C++ and Java, which can provide an efficient and incremental framework for exact real number computation. We propose to unify the B-adic and continued fraction approaches using our new representation. We aim to develop the notion of exact floating point in order to significantly improve the efficiency of basic arithmetic operations and establish a close relationship with the standard floating-point. We will analyse the complexity and improve the efficiency of our algorithms for all basic functions and obtain algorithms in the new framework for a variety of applications. We seek to implement all these algorithms in C++ and Java.
|
|
Key Findings |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Potential use in non-academic contexts |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Impacts |
|
| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
|
| Date Materialised |
|
|
|
|
Sectors submitted by the Researcher |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
| Project URL: |
|
| Further Information: |
|
| Organisation Website: |
http://www.imperial.ac.uk |