Description of the thesis topic

Modern applications in data analysis and scientific computing are characterized by significant volumes of data and extremely high operational complexity which make the use of supercomputers inevitable. Following recent technological developments, the architecture of high performance computers is becoming more and more heterogeneous, that is to say that the processors are often accompanied by specialized computing units capable of achieving very high performance but only on particular operations. A form of specialization is represented by low precision computing units such as half precision allowing to carry out calculations more efficiently (less time, memory and energy) but with a lower arithmetic precision. In this context, it is extremely important to design algorithms with low operational complexity and, at the same time, capable of using the computational power of modern computers by exploiting their heterogeneity. This stage will be interested in the study of mixed precision approximate linear algebra algorithms, that is, efficient algorithms, with low operational complexity based on the simultaneous use of several floating point arithmetics in order to take advantage of low precision units while providing guarantees on the overall accuracy of the solution.

- Activités du poste :

Mixed-precision low-rank approximations can be computed in two steps: first, a low-rank approximation is computed using only high precision using a pivoted QR factorization and then the resulting factors are partitioned in p groups and each group converted into the appropriate precision. The objective of this PhD is, instead, to develop a pivoted QR algorithm for computing directly a mixed-precisionrepresentation starting from the original matrix without the intermediate step. Multiple techniques can be combined to achieve this objective. First, the developed algorithm can, itself, use multiple computing precisions depending on how “important” is the data being computed; this will reduce the execution time and memory consumption for computing the final representation. Furthermore, approximate pivoting techniques, such as randomized pivoting or tournament pivoting, can be combined with mixed precision to achieve higher computation efficiency and better parallelism. The PhD can address multiple topics related to the above objective ranging from the design of such algorithms, conducting their rounding error analysis to provide bounds on the overall accuracy of the mixed-precision low-rank approximation and the actual implementation and experimental evaluation on parallel computers possibly equipped with GPUs using task-based parallel programming models.

Work Context

This PhD will be carried within the APO (Parallel Algorithms and Optimization) team of the IRIT (Institut de Recherche en Informatique de Toulouse) laboratory in the facilities of the ENSEEIHT school in Toulouse. It will be carried in the context of the national PEPR NumPEx (https://numpex.org/) Exa-SofT project, namely within task 4.3 of work-package 4.

The position is located in a sector under the protection of scientific and technical potential (PPST), and therefore requires, in accordance with the regulations, that your arrival is authorized by the competent authority of the MESR.