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Version 2.1.1

1st November 2023

HSL_MI20: Unsymmetric system: algebraic multigrid preconditioner

Given an \(n\times n\) sparse matrix \(\bf A\) HSL_MI20 has two functions.

  1. Given an \(n-\)vector \(\bf z\), HSL_MI20 computes the vector \({\bf x = Mz}\), where \(\bf M\) is an algebraic multigrid (AMG) v-cycle preconditioner for A.

  2. Alternatively, given a right-hand-side \(n-\)vector \(\bf b\), HSL_MI20 solves the linear system of equations \(\bf A x = b\) by an AMG method with or without a Krylov accelerator.

A classical AMG method is used, as described in [1] (see also Section 5 below for a brief description of the algorithm). The matrix \(\bf A\) must have positive diagonal entries and (most of) the off-diagonal entries must be negative (the diagonal should be large compared to the sum of the off-diagonals). During the multigrid coarsening process, positive off-diagonal entries are ignored and, when calculating the interpolation weights, positive off-diagonal entries are added to the diagonal.

Precision: At least 8-byte arithmetic is recommended.