Improving stability and performance: Integration of novel CholeskyQR2 into the ChASE library

Mijić, Nenad; Davidović, Davor; Xinzhe, Wu; Di Napoli, Edoardo Improving stability and performance: Integration of novel CholeskyQR2 into the ChASE library. In: SIAM Conference on Parallel Processing for Scientific Computing (PP24) (5 March 2024 - 8 March 2024) Baltimore, USA. (Unpublished)

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Abstract

The ChASE library is used to identify the extremal portion of dense Hermitian eigenvalue problems using the Chebyshev filter. It has been parallelised to support both homogeneous and heterogeneous architectures with distributed memory. In the latest code extension, the original Householder-based QR factorisation used to orthogonalise the filtered vectors has been replaced by the CholeskyQR2 algorithm. This algorithm, which is mainly implemented with level-3 BLAS operations, offers better adaptability to distributed memory systems than the Househoulder QR. However, CholeskyQR2 exhibits numerical instability for ill-conditioned matrices (with a condition number above 108), so one falls back to traditional Householder QR for ill-conditioned matrices. This presentation will focus on ongoing efforts to improve the numerical stability of ChASE QR factorisation. The first part will focus on the parallelisation of the novel CholeskyQR2 algorithm extended with the Gram-Schmidt method for distributed memory and GPU-based systems. The second part focuses on the integration of this novel QR factorisation algorithm into ChASE. The new algorithm shows improved performance and robustness regardless of the matrix condition number. Moreover, due to its design that constructs orthogonalised vectors by panels, it allows for a simpler and more efficient implementation of the updated QR in ChASE, significantly reducing the required flops.

Item Type:	Unpublished conference/workshop items or lecture materials
Uncontrolled Keywords:	CholeskyQR; QR factorisation; ChASE; eigensolvers; parallel processing; GPU, HPC cluster
Subjects:	NATURAL SCIENCES > Mathematics > Algebra TECHNICAL SCIENCES > Computing > Process Computing
Divisions:	Center for Informatics and Computing
Projects:	Project title Project leader Project code Project type Skalabilni algoritmi visokih performansi za buduće heterogene distribuirane računalne sustave-HybridScale Davor Davidović UIP-2020-02-4559 HRZZ National Competence Centres in the framework of EuroHPC Phase 2 Bastian Koller 101101903 EK
Depositing User:	Davor Davidović
Date Deposited:	12 Jun 2024 10:31
URI:	http://fulir.irb.hr/id/eprint/8763

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