Premium
Minimizing convex quadratics with variable precision conjugate gradients
Author(s) -
Gratton Serge,
Simon Ehouarn,
TitleyPeloquin David,
Toint Philippe L.
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.2337
Subject(s) - mathematics , conjugate gradient method , context (archaeology) , computation , conjugate , quadratic equation , matrix (chemical analysis) , mathematical optimization , regular polygon , variable (mathematics) , convex optimization , algorithm , mathematical analysis , geometry , paleontology , materials science , composite material , biology
Summary We investigate the method of conjugate gradients, exploiting inaccurate matrix‐vector products, for the solution of convex quadratic optimization problems. Theoretical performance bounds are derived, and the necessary quantities occurring in the theoretical bounds estimated, leading to a practical algorithm. Numerical experiments suggest that this approach has significant potential, including in the steadily more important context of multiprecision computations.