Numerická lineární algebra v POSIT aritmetice
| Thesis title in Czech: | Numerická lineární algebra v POSIT aritmetice |
|---|---|
| Thesis title in English: | Numerical linear algebra in POSIT arithmetic |
| Key words: | computer arithmetic|numerical linear algebra |
| English key words: | computer arithmetic|numerical linear algebra |
| Academic year of topic announcement: | 2024/2025 |
| Thesis type: | Bachelor's thesis |
| Thesis language: | |
| Department: | Department of Numerical Mathematics (32-KNM) |
| Supervisor: | doc. Erin Claire Carson, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 19.02.2025 |
| Date of assignment: | 19.02.2025 |
| Confirmed by Study dept. on: | 19.02.2025 |
| Guidelines |
| POSIT arithmetic is an alternative to the usual floating point number formats. In POSIT arithmetic, the number of bits used to represent each part of the finite precision number can vary. This makes it very interesting to study the numerical behavior of algorithms, especially iterative methods, using this new number format. The thesis will involve:
1) A literature review and background on finite precision number formats 2) An implementation of one or more algorithms using simulated POSIT arithmetic (e.g., in MATLAB) 3) An experimental study comparing the numerical behavior of the algorithms in POSIT arithmetic versus the usual floating point formats |
| References |
|
Gustafson, John L., and Isaac T. Yonemoto. "Beating floating point at its own game: Posit arithmetic." Supercomputing frontiers and innovations 4.2 (2017): 71-86. Buoncristiani, Nicholas, et al. "Evaluating the numerical stability of posit arithmetic." 2020 IEEE International Parallel and Distributed Processing Symposium (IPDPS). IEEE, 2020. Mallasén Quintana, David. "Leveraging Posits for the Conjugate Gradient Linear Solver on an Application-Level RISC-V Core." (2022). Higham, Nicholas J. Accuracy and stability of numerical algorithms. Society for industrial and applied mathematics, 2002. Available software: POSIT_toolbox, available at: https://gerard-meurant.fr/soft_meurant_n.html Gustafson, John. "Posit arithmetic." Mathematica Notebook describing the posit number system (2017). |
| Preliminary scope of work |
| POSIT arithmetic is a relatively recent alternative to floating point arithmetic. While much is understood about the behavior of numerical algorithms in floating point arithmetic, there is still much to discover about their properties in POSIT arithmetic. |
| Preliminary scope of work in English |
| POSIT arithmetic is a relatively recent alternative to floating point arithmetic. While much is understood about the behavior of numerical algorithms in floating point arithmetic, there is still much to discover about their properties in POSIT arithmetic. |