Fast method to compute the scalar product of gradient and given vector

@article{Fischer1989FastMT,
  title={Fast method to compute the scalar product of gradient and given vector},
  author={Herbert Fischer},
  journal={Computing},
  year={1989},
  volume={41},
  pages={261-265}
}
The paper deals with a special problem in Automatic Differentiation. Letf be a rational function ofn variables, let #(f) denote the number of operations to evaluatef(x), letg denote the gradient off. Many algorithms for minimizingf(x) require the scalar productg(u) tv. In the standard method for computingg(u) tv the amount of work grows withn·#(f). In this note a new method for computingg(u) tv is presented. The new method is considerably faster, its amount of work only grows with #(f). Die… CONTINUE READING

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