Reduced precision arithmetic for large sparse symmetric eigenvalue problems

• Κύριος συγγραφέας: Θανάσης, Ιωάννης
• Άλλοι συγγραφείς: Ioannis, Thanasis
• Γλώσσα: Greek
• Έκδοση: 2022
• Θέματα: Mixed precision; Symmetric eigenvalue problems; Jacobi Davidson; Μεικτή ακρίβεια; Ιδιοτιμές

Linear Algebra computations have been identified as a "computational giant" of statisticaldata analysis and data science. Indeed, many of the underlying data models necessitateextensive computations of this type. The Algebraic Eigenvalue Problem (AEP) is aprominent example of such computations. It is a classical problem, well studied and ofinterest in a range of areas much broader than Data Science. Over the years, a very largenumber of numerical algorithms, mathematical software libraries and high performancecomputing tools have been developed to deal with the AEP. A novel aspect that the fieldof Data Science brings in this rather mature area is that in its context, some subproblemsneed not to be performed in high accuracy. In this way, algorithm designers can exploitthe very high performance possible in recent processor architectures such as GPUs forcomputations running in floating-point precisions that are lower than the standard double(64-bit) and single (32-bit). Reduced accuracy is also sought because of other constraints,most notably the very high dimensionality of the problems and the need to reduce asmuch as possible the volume of data transferred between the storage hierarchy and theprocessors. In this thesis we examine the use of reduced precision arithmetic in the contextof the real symmetric eigenvalue problem. We focus on the well-known Jacobi-Davidsonalgorithm and show that implementations partly based on low precision arithmetic canobtain higher performance and can obtain results of similar accuracy as those obtained inimplementations using standard precisions. Extensive numerical experiments conductedin MATLAB using simulated low precision arithmetic on a large variety of matricesindicate that low precision arithmetic is a viable mode for increasing the performance ofthe specific algorithm.