Minimal Residual Methods for Solving Singular Hermitian, Complex Symmetric, or Skew Hermitian Linear Equations


Sou-Cheng Choi

13:30:00 - 14:20:00


Most existing Krylov subspace algorithms for linear systems assume non-singularity of the matrices or linear operators. MINRES-QLP (Choi, Paige, and Saunders 2011) is a MINRES-like algorithm but designed for computing the unique minimum-length and minimum-residual solutions of singular symmetric or Hermitian problems using efficient short-recurrent solution updates and stopping conditions. On nonsingular systems, MINRES-QLP is more stable than MINRES (Paige and Saunders 1975). In this talk we present a common framework that evolves similarly stable and effective algorithms for solving complex-symmetric, skew symmetric, and skew Hermitian linear systems or least-square problems.