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Version 1.1.0

20th March 2023

HSL_MI32: Symmetric possibly-indefinite system: MINRES method

This routine uses the MINRES method to solve the \(n \times n\) symmetric but possibly indefinite linear system \(\mathbf{Ax} = \mathbf{b}\), optionally using preconditioning. If \(\mathbf{M} = \mathbf{P} \mathbf{P} ^{T}\) is the preconditioning matrix, the routine actually solves the preconditioned system \[\bar{\mathbf{A}}\bar{\mathbf{x}} = \bar{\mathbf{b}},\] with \(\bar{\mathbf{A}} = \mathbf{P} \mathbf{A}\mathbf{P} ^{T}\) and \(\bar{\mathbf{b}} = \mathbf{P}\mathbf{b}\) and recovers the solution \(\mathbf{x} = \mathbf{P} ^{T} \bar{\mathbf{x}}\). Reverse communication is used for preconditioning operations and matrix-vector products of the form \(\mathbf{A}\mathbf{z}\).