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Do You Trust Derivatives or Differences?

Stefan M. Wild(wild***at***mcs.anl.gov)
Jorge J. Moré(more***at***mcs.anl.gov)

Abstract: We analyze the relationship between the noise level of a function and the accuracy and reliability of derivatives and difference estimates. We derive and empirically validate measures of quality for both derivatives and difference estimates. Using these measures, we quantify the accuracy of derivatives and differences in terms of the noise level of the function. An interesting consequence of these results is that the derivative of a function is not likely to have working precision accuracy for functions with modest levels of noise.

Keywords: Quality of Derivatives, Noisy Functions, Finite-Difference Methods

Category 1: Optimization Software and Modeling Systems (Optimization Software Design Principles )

Category 2: Optimization Software and Modeling Systems (Other )

Category 3: Other Topics (Optimization of Simulated Systems )

Citation: Argonne Mathematics and Computer Science Division Preprint ANL/MCS-P2067-0312, April 2012.

Download: [PDF]

Entry Submitted: 05/01/2012
Entry Accepted: 05/02/2012
Entry Last Modified: 05/01/2012

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