Parallel Selected Inversion of Block-Tridiagonal with Arrowhead Matrices

The inversion of structured sparse matrices is a fundamental yet computationally and memory-intensive task in many scientific applications, such as Bayesian statistical modeling and material science. In certain cases, only particular entries of the full inverse are required. This has motivated the d...

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Bibliographic Details
Published in:Proceedings / IEEE International Conference on Cluster Computing pp. 1 - 12
Main Authors: Maillou, Vincent, Gaedke-Merzhauser, Lisa, Ziogas, Alexandros Nikolaos, Schenk, Olaf, Luisier, Mathieu
Format: Conference Proceeding
Language:English
Published: IEEE 02.09.2025
Subjects:
Computational modeling
Distributed algorithms
Graphics processing units
Libraries
Linear algebra
Materials science and technology
Parallel algorithms
Predictive models
Selected linear algebra
Sparse matrices
Supercomputers
Temperature distribution
ISSN:2168-9253
Online Access:Get full text
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Summary:The inversion of structured sparse matrices is a fundamental yet computationally and memory-intensive task in many scientific applications, such as Bayesian statistical modeling and material science. In certain cases, only particular entries of the full inverse are required. This has motivated the development of so-called selected inversion algorithms (SIA), capable of computing only specific elements of the full inverse. Currently, most SIA implementations are restricted to shared-/distributed-memory CPU architectures or to single GPUs. Here, we introduce novel numerical methods to perform the parallel selected inversion and Cholesky decomposition of positive-definite, block-tridiagonal with arrowhead matrices. A distributed memory, GPU-accelerated implementation of our approach is presented and integrated into the structured solver library Serinv. We demonstrate its performance on synthetic and real datasets from statistical air temperature prediction models and achieve CPU (GPU) speedups of up to 2.6 \times(71.4 \times) over the SIA of the PARDISO library and up to 14 \times(380.9 \times) over the MUMPS library, when scaling to 16 processes.
ISSN:2168-9253
DOI:10.1109/CLUSTER59342.2025.11186484