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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Algorithm 937: MINRES-QLP for symmetric and Hermitian linear equations and least-squares problems

02/16/2014 12:41 PM

Abstract: We describe algorithm MINRES-QLP and its FORTRAN 90 implementation for solving symmetric or Hermitian linear systems or least-squares problems. If the system is singular, MINRES-QLP computes the unique minimum-length solution (also known as the pseudoinverse solution), which generally eludes MINRES. In all cases, it overcomes a potential instability in the original MINRES algorithm. A positive-definite preconditioner may be supplied. Our FORTRAN 90 implementation illustrates a design pattern that allows users to make problem data known to the solver but hidden and secure from other program units. In particular, we circumvent the need for reverse communication. Example test programs input and solve real or complex problems specified in Matrix Market format. While we focus here on a FORTRAN 90 implementation, we also provide and maintain MATLAB versions of MINRES and MINRES-QLP.

Algo 937 TOMS

Authors: Sou-Cheng Terrya Choi and Michael Alan Saunders

Keywords: Algorithms, Krylov subspace method, Lanczos process, conjugate-gradient method, singular least-squares, linear equations, minimum-residual method, pseudoinverse solution, ill-posed problem, regression, sparse matrix, data encapsulation

Publication: ACM Transactions on Mathematical Software (TOMS), 40(2), pp.1-12.

Webpage: https://doi.org/10.1145/2527267

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