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UID:submissions.pasc-conference.org_PASC24_sess174_pap107@linklings.com
SUMMARY:Arrowhead Factorization of Real Symmetric Matrices and its Applica
 tions in Optimized Eigendecomposition
DESCRIPTION:Paper\n\nMarcel Ferrari and Francesco Cavalli (ETH Zurich), Hu
 ssein el Harake (ETH Zurich / CSCS), and Christopher Lompa and Nicola Lo R
 usso (ETH Zurich)\n\nThis work introduces a new matrix decomposition, that
  we termed arrowhead factorization (AF). We showcase its applications as a
  novel method to compute all eigenvalues and eigenvectors of certain symme
 tric real matrices in the class of generalized arrowhead matrices. We pres
 ent a clear definition and proof by construction of the existence of AF, d
 etailing how to bridge the gap to full eigendecomposition. Our proposed me
 thod was tested against state-of-the-art routines, implemented in OpenBLAS
 , AOCL and Intel oneAPI MKL, using three synthetic benchmarks inspired by 
 real world scientific applications. These experiments highlighted up to 49
 x faster runtimes, proving the validity and efficacy of our approach. Furt
 hermore, we applied our method to a practical scenario by conducting a num
 erical experiment on simulation data derived from Golden-rule instanton th
 eory. This real world application showed a performance gain ranging from 2
 .5×, for exact eigendecomposition, to over 38× with the most aggressive ap
 proximation strategy, underscoring the efficiency, robustness and flexibil
 ity of our algorithm.\n\nDomain: Chemistry and Materials\n\nSession Chair:
  Sally Ellingson (University of Kentucky)
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