Serinv: A Scalable Library for the Selected Inversion of Block-Tridiagonal with Arrowhead Matrices
Additional information
Authors
Maillou V.,
Gaedke-Merzhaeuser L.,
Ziogas A. N.,
Schenk O.,
Luisier M.
Type
Article in conference proceedings
Year
2025
Language
English
Abstract
The inversion of structured sparse matrices is a key but computationally and memory-intensive operation in many scientific applications. There are cases, however, where only particular entries of the full inverse are required. This has motivated the development of so-called selected-inversion algorithms, capable of computing only specific elements of the full inverse. Currently, most of them are either shared-memory codes or limited to CPU implementations. Here, we introduce Serinv, a scalable library providing distributed, GPU-based algorithms for the selected inversion and Cholesky decomposition of positive-definite, block-tridiagonal arrowhead
matrices. This matrix class is highly relevant in statistical climate modeling and materials science applications. The performance of Serinv is demonstrated on synthetic and real datasets from statistical air temperature prediction models. In our numerical tests, Serinv achieves 32.3% strong and 47.2% weak scaling efficiency and up to two orders of magnitude speedup over the sparse direct solvers PARDISO and MUMPS on 16 GPUs.
Keywords
Selected inversion, Cholesky factorization, scalable algorithms, GPU implementation, structured sparse matrices
Conference proceedings
IEEE International Conference on Cluster Computing
Numero ( Mese )
September
Meeting name
IEEE International Conference on Cluster Computing
Meeting place
Edinburgh, United Kingdom
Meeting date
September 2nd-5th, 2025.
Pages (or article number)
1-12
