ABOUT THE AUTHOR

Sou-Cheng Choi, Ph.D.

Dr. Sou-Cheng T. Choi joined Kamakura as Chief Data Scientist on February 1, 2020. Dr. Choi previously served as the Principal Data Scientist and Lead Researcher in Machine Learning for the automotive and life innovation groups at Allstate Corporation, where she developed real-time risk models using advanced machine learning technology.

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MINRES-QLP: A Krylov Subspace Method for Indefinite or Singular Symmetric Systems

08/04/2011 02:33 PM

Authors: Sou-Cheng T. Choi, Christopher C. Paige, and Michael A. Saunders

Abstract: CG, SYMMLQ, and MINRES are Krylov subspace methods for solving symmetric systems of linear equations. When these methods are applied to an incompatible system (that is, a singular symmetric least-squares problem), CG could break down and SYMMLQ’s solution could explode, while MINRES would give a least-squares solution but not necessarily the minimum-length (pseudoinverse) solution. This understanding motivates us to design a MINRES-like algorithm to compute minimum-length solutions to singular symmetric systems. MINRES uses QR factors of the tridiagonal matrix from the Lanczos process (where R is upper-tridiagonal). MINRES-QLP uses a QLP decomposition (where rotations on the right reduce R to lower-tridiagonal form). On ill-conditioned systems (singular or not), MINRES-QLP can give more accurate solutions than MINRES. We derive preconditioned MINRES-QLP, new stopping rules, and better estimates of the solution and residual norms, the matrix norm, and the condition number.

MINRESQLP SISC 2011

Keywords: MINRES, Krylov subspace method, Lanczos process, conjugate-gradient method, minimum-residual method, singular least-squares problem, sparse matrix

Publication: SIAM Journal on Scientific Computing, 33(4), pp.1810-1836.

Webpage: https://doi.org/10.1137/100787921

ABOUT THE AUTHOR

Sou-Cheng Choi, Ph.D.

Dr. Sou-Cheng T. Choi joined Kamakura as Chief Data Scientist on February 1, 2020. Dr. Choi previously served as the Principal Data Scientist and Lead Researcher in Machine Learning for the automotive and life innovation groups at Allstate Corporation, where she developed real-time risk models using advanced machine learning technology.

Read More