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• W1666670079 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." @default.
• W1666670079 created "2016-06-24" @default.
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• W1666670079 date "2011-01-01" @default.
• W1666670079 modified "2023-10-18" @default.
• W1666670079 title "MINRES-QLP: A Krylov Subspace Method for Indefinite or Singular Symmetric Systems" @default.
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• W1666670079 doi "https://doi.org/10.1137/100787921" @default.
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