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DTSTAMP:20250822T115806Z
LOCATION:Campussaal - Plenary Room
DTSTART;TZID=Europe/Stockholm:20250616T102000
DTEND;TZID=Europe/Stockholm:20250616T105000
UID:submissions.pasc-conference.org_PASC25_sess149_pos146@linklings.com
SUMMARY:P20 - GPU-Accelerated Matrix Decomposition and Selected Inversion 
 for Banded Arrowhead Matrices
DESCRIPTION:Carla Lopez Zurita (ETH Zurich); Lisa Gaedke-Merzhäuser (King 
 Abdullah University of Science and Technology, Università della Svizzera i
 taliana); Vincent Maillou (ETH Zurich); and Olaf Schenk (Università della 
 Svizzera italiana)\n\nMatrix inversion is a fundamental operation in linea
 r algebra which arises in various scientific problems. Many applications a
 re cast as sparse linear systems, however, when inverted, they produce den
 se matrices. In some cases, only a subset of the complete inverse—referred
  to as selected inverse—is required. This approach is especially relevant 
 in fields like statistical learning and nano-electronics, where the underl
 ying sparse matrices of interest often exhibit a banded arrowhead sparsity
  pattern or can be efficiently permuted to one. Efficient, GPU-accelerated
 , implementations for the selected inversion of block tridiagonal arrowhea
 d matrices exist within the Serinv library. Our work builds upon this foun
 dation by extending the existing selected inversion routines to cover rela
 ted sparsity patterns, such as banded arrowhead and n-block diagonal arrow
 head matrices. Banded implementations only work with non-zero elements of 
 the matrix but are challenging to implement efficiently on GPUs. To addres
 s this, we explore an n-block diagonal tiling approach. Although this meth
 od may introduce some zero elements, it allows for greater efficiency, and
  is well-suited for parallelization on GPUs. We rely on Python for ease of
  use and compatibility, alongside CuPy for efficient GPU computations. Thi
 s combination enables us to deliver scalable and high-performance solution
 s for selected inversion tasks.\n\nSession Chair: Chris Cantwell (Imperial
  College London)\n\n
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