Computational graphs for matrix functions

Many numerical methods for evaluating matrix functions can be naturally viewed as computational graphs. Rephrasing these directed acyclic graphs (DAGs) is a particularly effective approach to study existing techniques, improve them, and eventually derive new ones. The accuracy of techniques characterized by the their scalar counterparts, thus designing algorithms regarded scalar-valued optimization problem. derivatives needed during calculated automatically exploiting structure DAG in fashion analogous backpropagation. This article describes GraphMatFun.jl , Julia package that offers means generate manipulate graphs, optimize coefficients, Julia, MATLAB, C code evaluate them efficiently at argument. software also provides tools estimate graph-based algorithm obtain numerically reliable methods. For exponential, example, using particular form (degree-optimal) polynomials produces implementations many cases are cheaper, terms cost, than Padé-based typically used mathematical software. optimized corresponding generated available online.