Parallel Selected Inversion of Block-Tridiagonal with Arrowhead Matrices


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Date

2025

Publication Type

Conference Paper

ETH Bibliography

yes

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Abstract

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×(71.4×) over the SIA of the PARDISO library and up to 14×(380.9×) over the MUMPS library, when scaling to 16 processes.

Publication status

published

Editor

Book title

2025 IEEE International Conference on Cluster Computing (CLUSTER)

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Volume

Pages / Article No.

Publisher

IEEE

Event

IEEE International Conference on Cluster Computing (CLUSTER 2025)

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Methods

Software

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Date created

Subject

Selected linear algebra; Distributed algorithms; Linear algebra; Sparse matrices

Organisational unit

03925 - Luisier, Mathieu / Luisier, Mathieu check_circle

Notes

Funding

209358 - Quantum Transport Simulations at the Exascale and Beyond (QuaTrEx) (SNF)

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