What Color Is Your Jacobian? Graph Coloring for Computing Derivatives

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A probing method for computing the diagonal of a matrix inverse (2012, methodology): “Based on this architecture, solving a linear system can be readily parallelized (see, e.g. [42]), S ( A p ) can be computed efﬁciently, parallel graph coloring algorithms can be found in [40], and the construction of and computations with V s can be well parallelized as well.”
Effective adjoint approaches for computational fluid dynamics (2019, background): “Similar to the single-cell residual approach, graph coloring [155] exploits the sparsity of Jacobian matrices and requires the identification of the stencil of each residual computation.”
CasADi: a software framework for nonlinear optimization and optimal control (2018, methodology): “The coloring algorithms inCasADi are used togetherwith a largest-first preordering step [50,136].”
A General-Purpose Software Framework for Dynamic Optimization (Een algemene softwareomgeving voor dynamische optimalisatie) (2013, neutral): “1] with a largest-first ordering [86, 183](7).”
OpenMDAO: an open-source framework for multidisciplinary design, analysis, and optimization (2019, background): “There are a wide variety of serial coloring algorithms [97, 56, 55, 18, 28], originally developed for coloring partial derivative Jacobians.”