Randomized Heuristics for Exploiting Jacobian Scarcity

Griewank and Vogel introduced the notion of Jacobian scarcity, which generalizes the properties of sparsity and rank to capture a kind of deficiency in the degrees of freedom of the Jacobian matrix $F\u27(mathbf{x}).$ We describe new randomized heuristics that exploit scarcity for the optimized evaluation of collections of Jacobian-vector or Jacobian-transpose-vector products