Computational implementations for solving systems of linear equations often rely on a one-size-fits-all approach based on LU decomposition of dense matrices stored in column-major format. Such solvers are typically implemented with the aid of the xGESV set of functions available in the low-level LAPACK software, with the aim of reducing development time by taking advantage of well-tested routines. However, this straightforward approach does not take into account various matrix properties which can be exploited to reduce the computational effort and/or to increase numerical stability. Furthermore, direct use of LAPACK functions can be error-prone for non-expert users and results in source code that has little resemblance to originating mathematical expressions. We describe an adaptive solver that we have implemented inside rece
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