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ODE‐based double‐preconditioning for solving linear systems A α x = b and f ( A ) x = b
Author(s) -
Antoine Xavier,
Lorin Emmanuel
Publication year - 2021
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2399
Subject(s) - ode , mathematics , linear system , computation , ordinary differential equation , extension (predicate logic) , matrix (chemical analysis) , linear differential equation , coefficient matrix , system of linear equations , algebraic number , algebra over a field , algorithm , differential equation , pure mathematics , mathematical analysis , computer science , eigenvalues and eigenvectors , materials science , physics , quantum mechanics , composite material , programming language
This article is devoted to the computation of the solution to fractional linear algebraic systems using a differential‐based strategy to evaluate matrix–vector productsA α x , with α ∈ ℝ + ∗. More specifically, we propose ODE‐based preconditioners for efficiently solving fractional linear systems in combination with traditional sparse linear system preconditioners. Different types of preconditioners are derived (Jacobi, incomplete LU, Padé) and numerically compared. The extension to systems f ( A ) x = b is finally considered.