The module HSL_MA42 solves one or more sets of sparse linear equations, $Ax=b$ or ${A}^{T}x=b$, by the frontal method, optionally using direct-access ﬁles for the matrix factors. Use is made of high level BLAS kernels. The code has low in-core memory requirements. The matrix $A$ may be input by the user in either of the following ways:
In both cases, the coeﬃcient matrix and right-hand side(s) are of the form
$$A=\sum _{k=1}^{m}{A}^{\left(k\right)},\phantom{\rule{2em}{0ex}}b=\sum _{k=1}^{m}{b}^{\left(k\right)}.$$
In case (i), the summation is over ﬁnite elements. The matrix ${A}^{\left(k\right)}$ is nonzero only in those rows and columns which correspond to variables in the $k$-th element. The vector ${b}^{\left(k\right)}$ is nonzero only in those rows which correspond to variables in element $k$.
In case (ii), the summation is over equations and ${A}^{\left(k\right)}$ and ${b}^{\left(k\right)}$ are nonzero only in row $k$.