Version 1.0.0
12th July 2004 User documentation
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HSL_MI02: Symmetric possiblyindefinite system: SYMMBK method
This routine uses the SYMMBK method to solve the \(n \times n\) symmetric but possibly indefinite linear system \(\mathbf{Ax} = \mathbf{b}\), optionally using preconditioning. If \(\mathbf{P} \mathbf{P} ^T\) is the preconditioning matrix, the routine actually solves the preconditioned system
\[\mathbf{\bar{A}\bar{x}} = \bar{\mathbf{b}},\]
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 matrixvector products of the form \(\mathbf{Az}\).