AUTOMATIC EVALUATIONS OF CROSS-DERIVATIVES

作者：Griewank Andreas^*; Lehmann Lutz; Leovey Hernan; Zilberman Marat

来源：Mathematics of Computation, 2014, 83(285): 251-274.

Cross-derivatives are mixed partial derivatives involving at most one differentiation in each one of n coordinate directions. They are a computational tool in combinatorics and of potential use in high-dimensional integration. Here we present two methods that evaluate all 2(n) cross-derivatives at a given point. The computational complexity is, respectively, 3(n) and n(2)2(n) times that of the underlying function. The asymptotically faster method involves a final interpolation step, which can easily be carried out using extra-accurate subtractions to reduce the effect of numerical round-off. Further complexity reductions for large n can be obtained through faster polynomial multiplications, e.g., Karatsuba's method or FFT.

• 出版日期2014-1