Work

Deriving Algorithms for Triangular Tridiagonalization a Skew-Symmetric Matrix

Year: 2023

Type: preprint

Abstract: This paper provides technical details regarding the application of the FLAME methodology to derive algorithms hand in hand with their proofs of correctness for the computation of the $ L T L^T $ decomposition (with and without pivoting) of a skew-symmetric matrix. The approach yields known as well as new algorithms, presented using the FLAME notation, enabling comparing and contrasting. A number of BLAS-like primitives are exposed at the core of the resulting unblocked and blocked algorithms.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2311.10700

Authors: van de Geijn, Robert, Myers, Maggie, Xu, RuQing G., Matthews, Devin

Institutions: The University of Texas at Austin, The University of Tokyo, Southern Methodist University

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, U.S. Department of Energy, University of Texas at Austin, University of Tokyo, Division of Chemistry

Awards: CAREER: Tensor Factorization Methods for High-Level Electronic Structure Theory, Collaborative Research: Frameworks: Beyond the BLAS: A Framework for Accelerating Computational and Data Science, PRACTICAL TENSOR HYPERCONTRACTION COUPLED CLUSTER METHODS FOR EXCITED STATE DYNAMICS, Collaborative Research: Frameworks: Beyond the BLAS: A framework for accelerating computational and data science, G6128383262, G774187239

OpenAlex ID: W4388844338

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